TRANSPORT PROPERTIES of GRAPHENE BASED VAN DER WAALS HETEROSTRUCTURES Geliang Yu

TRANSPORT PROPERTIES OF GRAPHENE BASED VAN DER

WAALS HETEROSTRUCTURES

Geliang Yu

A THESIS SUBMITTED TO THE UNIVERSITY OF MANCHESTER

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES

School of Physics & Astronomy

Manchester 2015

Geliang Yu

Abstract

In the past few years, led by graphene, a large variety of two dimensional (2D) materials have been discovered to exhibit astonishing properties. By assembling 2D materials with different designs, we are able to construct novel artificial van der Waals (vdW) heterostructures to explore new fundamental physics and potential applications for future technology.

This thesis describes several novel vdW heterostructures and their fundamental properties. At the beginning, the basic properties of some 2D materials and assembled vdW heterostructures are introduced, together with the fabrication procedure and transport measurement setups. Then the graphene based capacitors on hBN (hexagonal Boron Nitride) substrate are studied, where quantum capacitance measurements are applied to determine the density of states and many body effects.

Meanwhile, quantum capacitance measurement is also used to search for alternative substrates to hBN which allow graphene to exhibit micrometer-scale ballistic transport. We found that graphene placed

2 on top of MoS2 and TaS2 show comparable mobilities up to 60,000cm /Vs. After that, the graphene/hBN superlattices are studied. With a Hall bar structure based on the superlattices, we find that new Dirac minibands appear away from the main Dirac cone with pronounced peaks in the resistivity and are accompanied by reversal of the Hall effects. With the capacitive structure based on the superlattices, quantum capacitance measurement is used to directly probe the density states in the graphene/hBN superlattices, and we observe a clear replica spectrum, the Hofstadter-butterfly fan diagram, together with the suppression of quantum Hall Ferromagnetism. In the final part, we report on the existence of the valley current in the graphene/hBN superlattice structure. The topological current originating from graphene’s two valleys flows in opposite directions due to the broken inversion symmetry in the graphene/hBN superlattice, meaning an open band gap in graphene.

静以修身，俭以养德，非澹泊无以明志，非宁静无以致远。

-诸葛亮

Contents

Declaration ...... iii

Acknowledgements ...... v

Publications ...... viii

Abbreviation ...... 1

List of figures ...... 2

PREAMBLE ...... 8

Part I Introduction ...... 10

Chapter 1 Introduction to van der Waals heterostructures ...... 11

1.1 Introduction to 2D materials ...... 12

1.11 Graphene ...... 12

1.12 Hexagonal boron nitride (hBN) ...... 22

1.13 Transition metal dichalcogenides ...... 25

1.14 Other 2D materials ...... 27

1.2 VdW heterostructures ...... 30

1.21 Vertical heterostructures ...... 30

1.22 Graphene/hBN superlattice ...... 32

Chapter 2 Fabrication of vdW heterostructure based devices and experimental setup ...... 37

2.1 Preparing flakes ...... 38

2.11 Mechanical exfoliation ...... 38

2.12 CVD method ...... 39

2.2 VdW heterostructure device fabrication ...... 41

2.2.1 Making vdW heterostructures ...... 41

2.2.2 Superlattice alignment ...... 44

2.2.3 Annealing process ...... 45

2.2.4 Lithography process ...... 46

2.2.5 Hall bar structure ...... 48

2.2.6 Capacitive structure ...... 50

2.3 Measurement setup ...... 52

2.3.1 Helum-3 rotating probe ...... 52

2.3.2 Resistive measurement ...... 53

2.33 Capacitive measurement ...... 55

Part II Experimental results ...... 58

Chapter 3 Interaction phenomena in graphene seen through quantum capacitance ...... 59

Chapter 4 Electronic properties of graphene encapsulated with different two-dimensional atomic crystals ...... 60

Chapter 5 Cloning of Dirac fermions in graphene superlattices ...... 61

Chapter 6 Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices ...... 62

Chapter 7 Detecting topological current in graphene superlattices...... 63

Chapter 8 Conclusion ...... 64

Bibliography ...... 65

Declaration

No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institution of learning.

iii

1. The author of this thesis (including any appendices and/or schedules to this thesis)

owns any copyright in it (the “Copyright”) and he has given The University of

Manchester the right to use such Copyright for any administrative, promotional,

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with the regulations of the John Rylands University Library of Manchester. Details of

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which may be described in this thesis, may not be owned by the author and may be

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and must not be made available for use without the prior written permission of the

owner(s) of the relevant Intellectual Property Rights and/or Reproductions.

4. Further information on the conditions under which disclosure, publication and

exploitation of this thesis, the Copyright and any Intellectual Property Rights and or

Reproductions described in it may take place is available from the Head of School of

Physics and Astronomy.

Acknowledgements

I would like to thank my supervisor Prof. Kostya Novoselov for bringing me into this fantastic research, and giving me lots of guidance and support in my work and personal life.

Your enthusiasm and talent in science, technology and art have set a great example to me.

And you are always thinking of the best for me, like the water with the highest level of good.

And also I have heartfelt appreciation to my patient and kind co-supervisor Prof. Andre Geim who has opened my mind, guiding me through the projects, giving me ideas and inspiring me to have ‘brain’ in the past four years. Your optimistically fighting with the mysterious world of science like a knight always impresses me, and definitely will benefit me for the rest of my life time (including the humorous and ‘mocking’ style ).

Great appreciation also goes to Daniel Cunha-Elias and Alexander Mayorov for bringing me in the game and patiently guiding me through the experiments, the data analysis and the figures preparation. Also to Artem Mishchenko, thanks a lot for your friendly help and priceless suggestion in the experiments, especially the super cool cold bridge.

I must also thank the people in the fabrication part of our group for patiently teaching and helping me through the complicated fabrication steps. And specifically to the genius people who have designed and provided me with so many amazing devices. They are Zhixian Tu,

Branson Belle, Rashid Jali, Roma Gorbachev, Andrey Kretinin, Yang Cao, Fred Withers,

Moshe Ben Israel, and Ekaterina Khestanova. I have such good luck to work with your guys.

I should also thank our great theoretical collaborators for looking at our experimental data and helping to understand the beautiful physics, they are Prof. Leonid Levitov, Prof. Vladimir

Falko, Prof. Boris Shklovskii, Prof. Paco Guinea, Justin Song and Brian Skinner.

Collaborating with your guys is so amazing. I do appreciate that.

Also to my talented and enthusiastic colleagues and friends, who have been helping and accompanying me during the PhD. They are Liam Britnell, Roshan Krishna Kumar, Da Jiang,

Colin Woods, Leonid Ponomarenko, Axel Eckmann, Yong Jin Kim, Sheng Hu, Alexander

Zhukhov, Thanasis Georgiou, Jaesung Park, I-Ling Tsia, Swee-Liang Wong, Marcelo Lozada,

Peter Blake, Recep Zan, Peng Tian, Kaige Zhou, Yang Su, James Chapman, Aravind

Vijayaraghavan and Antonios Oikonomou.

Also to my parents, my wife, my grandma, my uncles and aunts and my brothers for their constant love, encouragements and supports all the time. I hope this PhD makes you happy.

Also to my grandpa, there was so much fun in my childhood with you. I will remember you forever.

Manchester, June 2015

Dedicated to Yanyan, Jinlian, Qihu

vii

Publications

 Interaction phenomena in graphene seen through quantum capacitance

G. L. Yu, R. Jalil, Branson Belle, Alexander S. Mayorov, Peter Blake, Frederick Schedin, Sergey

V. Morozov, Leonid A. Ponomarenko, F. Chiappini, S. Wiedmann, Uli Zeitler, Mikhail I.

Katsnelson, A. K. Geim, Kostya S. Novoselov, and Daniel C. Elias

PNAS, 110, 3282-3286 (2013)

 Cloning of Dirac fermions in graphene superlattices

L. A. Ponomarenko, R. V. Gorbachev, G. L. Yu, D. C. Elias, R. Jalil, A. A. Patel, A. Mishchenko,

A. S. Mayorov, C. R. Woods, J. R. Wallbank, M. Mucha-Kruczynski, B. A. Piot, M. Potemski, I.

V. Grigorieva, K. S. Novoselov, F. Guinea, V. I. Fal’ko & A. K. Geim

Nature, 497, 594–597 (2013)

 Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene

superlattices

G. L. Yu, R. V. Gorbachev, J. S. Tu, A. V. Kretinin, Y. Cao, R. Jalil, F.Withers,

L.A.Ponomarenko, B. A. Piot, M. Potemski, D. C. Elias, X. Chen, K.

Watanabe, T. Taniguchi, I. V. Grigorieva, K. S. Novoselov, V. I. Fal’ko, A. K. Geim & A.

Mishchenko

Nature Physics 10, 525–529 (2014)

 Detecting topological currents in graphene superlattices

R. V. Gorbachev, J. C. W. Song, G. L. Yu, A. V. Kretinin, F. Withers, Y. Cao, A. Mishchenko, I.

V. Grigorieva, K. S. Novoselov, L. S. Levitov, A. K. Geim

Science, 24, 6208 (2014)

viii

 Commensurate–incommensurate transition in graphene on hexagonal boron nitride

C. R. Woods, L. Britnell, A. Eckmann, R. S. Ma, J. C. Lu, H. M.

Guo,X. Lin, G. L. Yu, Y. Cao, R. V. Gorbachev, A. V. Kretinin, J. Park, L.

A. Ponomarenko, M. I. Katsnelson, Yu. N. Gornostyrev, K. Watanabe, T.

Taniguchi, C. Casiraghi, H-J. Gao, A. K. Geim & K. S. Novoselov

Nature Physics, 10, 451–456 (2014)

 Electronic Properties of Graphene Encapsulated with Different Two-Dimensional Atomic

Crystals

V. Kretinin, Y. Cao, J. S. Tu, G. L. Yu, R. Jalil, K. S. Novoselov, S. J. Haigh, A. Gholinia, A.

Mishchenko, M. Lozada, T. Georgiou, C. R. Woods, F. Withers, P. Blake, G. Eda, A. Wirsig,

C. Hucho, K. Watanabe, T. Taniguchi, A. K. Geim, and R. V. Gorbachev

Nano Letter, 14, 3270–3276 (2014)

 Effect of dielectric response on the quantum capacitance of graphene in a strong magnetic

field

Brian Skinner, G. L. Yu, A. V. Kretinin, A. K. Geim, K. S. Novoselov, and B. I. Shklovskii

Phys. Rev. B, 88, 155417 (2013)

 Quantum capacitance measurements of electron-hole asymmetry and next-nearest-neighbor

hopping in graphene

A. Kretinin, G. L. Yu, R. Jalil, Y. Cao, F. Withers, A. Mishchenko, M. I. Katsnelson, K. S.

Novoselov, A. K. Geim, and F. Guinea

Phys. Rev. B 88, 165427 (2013)

 Raman Fingerprint of Aligned Graphene/h-BN Superlattices

Axel Eckmann, Jaesung Park, Huafeng Yang, Daniel Elias, Alexander S. Mayorov, Geliang

Yu, Rashid Jalil, Kostya S. Novoselov, Roman V. Gorbachev, Michele Lazzeri, Andre K.

Geim, and Cinzia Casiraghi

Nano Letters, 13, 5242–5246 (2013)

 Raman Modes of MoS2 Used as Fingerprint of van der Waals Interactions in 2D Crystal-

Based Heterostructures

K-G Zhou, F. Withers, Y. Cao, S. Hu, G. Yu, and C. Casiraghi

ACS Nano, 8, 9914–9924(2014)

 Quality heterostructures from two dimensional crystals unstable in air by their assembly in

inert atmosphere

Y. Cao, A. Mishchenko, G. L. Yu, K. Khestanova, A. Rooney, E. Prestat, A. V. Kretinin, P.

Blake, M. B. Shalom, G. Balakrishnan, I. V. Grigorieva, K. S. Novoselov, B. A. Piot, M.

Potemski, K. Watanabe, T. Taniguchi, S. J. Haigh, A. K. Geim, R. V. Gorbachev

Submitted to Nature Communication

 Nonlocal transport in few-layer black phosphorus due to in-plane conductance anisotropy.

G. L. Yu .et al. (Under preparation)

Abbreviation

2D: two dimensional hBN: hexagonal Boron Nitride vdW; van der Waals

MoS2: Molybdenum disulphide

SiO2: Silicon dioxide

MoS2: Molybdenum disulphide

WS2: Tungsten disulphide

MoSe2: Molybdenum diselenide

WSe2: Tungsten diselenide

NbSe2: Niobium diselenide

TaS2: Molybdenum disulphide

BISCCO: Bismuth Strontium Calcium Copper Oxide

STEM: Scanning transmission electron microscopy

AFM: Atomic Force Microscope

Au: Gold

CVD: Chemical Vapor Deposition

H2: Hydrogen

Ar: Argon

CH4: Methane

DI water: De-Ionized water

PMGI: Poly Methyl GlutarImide

PMMA: Poly Methyl MethAcrylate

AC: Alternating current

VTI: Variable temperature inserts

List of figures

Figure 1.1 Carbon allotropes including 0D Fullerene, 1D Carbon Nanotube, 2D graphene and 3D

Graphite...... 13

Figure 1.2 (a) A honeycomb lattice with subblattices A and B shown in black and grey. (b) Reciprocal lattice vectors and some special points in the Brillouin zone. (adapted from reference [73] ) ...... 14

Figure 1.3 The Electron energy spectrum of graphene dispersion. Right: Zoom-in of the electronic structure at K point. (Adapted from reference [72]) ...... 15

Figure 1.4 (a) Schematic of graphene Hall bar device on SiO2 substrate. (b) Ambipolar Electric Field effect in graphene. The inserts show the changing positions of Fermi level as function of gate voltages.

(Adapted from reference [87]) ...... 18

Figure 1.5 (a) Schematic of high mobility sample with 1D contact. (b) Four-terminal resistivity measured from a 15μm × 15μm device fabricated by the vdW assembly technique with edge-contacts.

Low-temperature response is shown in the right inset. A negative resistance is observed, indicating ballistic transport. (Adapted from reference [70]) ...... 19

Figure 1.6 In the quantum Hall regime, electrons travel through the edge only...... 19

Figure 1.7 Integer quantum Hall effect in graphene. ρxx and σxy as a function of the carrier density n at

124T. (Adapted from reference [12]) ...... 20

Figure 1.8 High mobility suspend graphene is studied focusing on the many body effect at high magnetic field, showing integer QHE and FQHE. (a) The scanning single electron transistor (SET) is

~100 nm in size and is held 50 to 150 nm above the graphene flake. The red arrow indicates the path of the spatial scans. (b) Inverse compressibility dμ/dn as a function of carrier density n and magnetic field B. (c) Data from (b) plotted as a function of filling factor ν. Vertical features correspond to quantum Hall states, whereas localized states curve as the magnetic field is changed. (Adapted from reference [93])...... 22

Figure 1.9 (a) Schematic of hBN structures. (b) hBN flake prepared by mechanical exfoliation,

Different layers of hBN could be noticed from monolayer to bulk, the scale bar is 20um...... 23

Figure 1.10 (a) AFM image of monolayer graphene on hBN with electrical leads. White dashed lines indicate the edge of the graphene flake. Scale bar, 2 µm. (b) Histogram of the height distribution

(surface roughness) measured by AFM for SiO2 (black triangles), h-BN (red circles) and graphene-on-

BN (blue squares). Solid lines are Gaussian fits to the distribution. Inset: high-resolution AFM image showing a comparison of graphene and hBN surfaces, corresponding to the dashed square in a. Scale bar, 0.5 µm. (Adapted from reference [13]) ...... 24

Figure 1.11 (a) Characteristic I-V curves for graphite/hBN/graphite devices with different thicknesses of hBN insulating layer. (b) Exponential dependence of zero-bias resistance on the thickness of hBN separating graphite electrodes (1 to 4 layers of hBN, 0.3-1.3 nm). (Adapted from reference [14]) ..... 25

Figure 1.12 (a) Schematic of MoS2 structure. Sulphur atom coloured with yellow and Molybdenum coloured with black. The layer distance is 0.65 nm. (Adapted from reference [23]) (b) An optical image of MoS2 flakes on top of PMMA. Different layers of MoS2 are also observed...... 26

Figure 1.13 (a) I-V curve for MoS2 transistor with bias voltage from 10mV to 500 mV at room- temperature, showing an on/off ratio up to 108. (Adapted from reference [23]) (b) Longitudinal resistance Rxx (red curve) and Hall resistance Rxy (blue curve) of an hBN-encapsulated CVD 1L

2 MoS2 device with graphene contacts. The mobility for monolayer MoS2 is around 1000 cm /Vs.

(Adapted from reference [115]) ...... 27

Figure 1.14 Classified 2D materials. Monolayers proved to be stable under ambient conditions (room temperature in air) are shaded blue; those probably stable in air are shaded green; and those unstable in air but that may be stable in inert atmosphere are shaded pink. Grey shading indicates 3D compounds that have been successfully exfoliated down to monolayers, as is clear from atomic force microscopy. (Adapted from reference [3]) ...... 28

Figure 1.15 (a) R–T curves for graphene/BISCCO vdW heterostructures measured at applied bias currents of Idc=0, 0.04, 0.08, 0.16, 0.20, 0.24, 0.28, 0.32 and 0.36 mA, showing a Tc around 88K.

Inset: the schematic of the sample and transport measurement, where BISCCO is encapsulated with graphene and Au contacts is on top of the graphene, bringing the non-zero value of resistance below

88K. (Adapted from [128]) (b) Schematics of our NbSe2 sample, where NbSe2 is placed on hBN and covered with thin hBN. Down left is a cross sectrionl bright field STEM image of a bulk hBN /

bilayer NbSe2 / bulk hBN with the extracted interlayer distances on the right. Centre – Superimposed

STEM-EELS image with elemental profiles for the niobium–M4, 5 edge (orange) and selenium-L3 edge (green). (c) Tc of NbSe2 changes with thickness. The dotted line in the inset is a guide to the eye.

...... 29

Figure 1.16 Building vdW heterostructures...... 30

Figure 1.17 (a) Schematic of a Tunnelling transisotr device. Top hBN is as the encapsulation layer; bottom hBN is used as the substrate and the middle hBN functions as a tunnel barrier. (b) I-Vs for different Vg (in 10V steps). (Adapted from reference [101]) ...... 31

Figure 1.18 (a) Schematic of our devices and measurements methods. The current flows only along the top graphene Hall bar layer, and the drag signal is detected from the bottom graphene. The spacer between the two layers is 1nm. (b) ρdrag as a function of VT and VB. The black curves indicate zero- lines of ρdrag; the colour scale is ±60Ω. (Adapted from reference [130]) ...... 32

Figure 1.19 Hofstadter’s butterfly. (Theory behaviour of electrons in 2D lattice at a filed. x-axis is the flux quantum, y-axis is the energy)...... 33

Figure 1.20 Graphene/hBN superlattice with different periodicity. (a)-(c) schematics of the alignment between graphene (blue) and hBN (black) with rotation degree 3o(a), 1o(b) and 0o(c); λ is the periodicity. (d)-(f) STM topography images showing 2.4nm(d), 6nm(e) and 11.5nm(f) moiré patterns.

(Adapted from reference [83]) ...... 34

Figure 1.21 The gap issue at the neutrality point. (a) Temperature dependences of minimum conductivity at the main and secondary NPs show no-gap behaviour. The electron-side NP is scaled by a factor of 20. (Adapted from reference [134]) (b) Gaps measured by thermal activation at the CNP and hole satellite peak positions with 4 different devices. (Adapted from reference [137]) (c)

Correlation of observed band gaps with moiré wavelength λ. (Adapted from reference [85]) (d)

Longitudinal resistivity as a function of carrier concentration for non-encapsulated graphene on hBN with the 14 nm moiré pattern for a range of temperatures. The insert is for an encapsulated device with the same moiré pattern. (e) Temperature dependence of the conductivity minimum for the measurement in (d), red circle is for the non-encapsulated sample and blue is for the encapsulated

device, shows that the gap is available for non-encapsulated device with Δ/2 ≈ 180 K. (Adapted from reference [138] ) ...... 35

Figure 2.1 (a) An optical image of graphene on SiO2/Si substrate. (b) Graphene on PMMA/PMGI surface. (c) hBN flake on SiO2/Si substrate. (d) The optical image of hBN on PMMA/PMGI. The scale bars are 10um...... 39

Figure 2.2 CVD system for graphene production...... 40

Figure 2.3 CVD graphene. (a) CVD Graphene on SiO2. (b) CVD graphene on PMMA...... 40

Figure 2.4 ‘Wet’ transfer. (a) Graphene is placed on top of SiO2 by mechanical exfoliation. (b)

PMMA is spun on top of the graphene flake. (c) Tape with a window is attached to PMMA with graphene flake in the middle of the window. (d) Structure is dipped in KOH to dissolve the SiO2 substrate. After the chemical reaction for the substrate, the graphene flake with the PMMA and the tape will be suspend on top of KOH. (e) Graphene flake is then cleaned in DI water...... 42

Figure 2.5 Dry transfer processes. (a) PMMA/PMGI resists are spun on top of Si wafer first, and then graphene flake is exfoliated on top of the resists. (b) Around the middle of the flake, the resist is scratched to make path for MF-319 to the bottom PMGI. (c) PMGI resist is dissolved, leaving the top graphene flake and PMMA floating...... 43

Figure 2.6 Transfer processes after preparing flakes on PMMA. (a) Turn the flake to face the target area. (b) Attach the flake to the target flake gradually. (c) Remove the top PMMA...... 44

Figure 2.7 (a) The schematic hexagonal lattice with armchair (red dash lines) and zigzag (purple dash lines) edge. (b) Edges of typical hBN flake with different edges. It can be either armchair or zigzag edge along the yellow directions...... 45

Figure 2.8 (a) Image of an alignment between graphene and hBN flake. (b) Moiré pattern with a superlattice length of 12nm from AFM measurement for the aligned sample shown in the red square in the left image...... 45

Figure 2.9 The schematic procedure for device fabrication with photolithography. (a) Photoresist coating with a bi-layer photoresist: PMGI and S-1805. (b) Exposure of the pattern with the

LaserWriter. Photolithography uses photoresist with ultraviolet light. (c) Development after the exposure. (d) Deposition the metals for the contacts. (e) Lift-off procedure. (f) Etching Mesa with

Plasma...... 46

Figure 2.10 (a) The schematic of Hall bar structure. (b) Graphene-based Hall bar structure sits on top of hBN substrate and is encapsulated by hBN...... 49

Figure 2.11 The optical images of fabricated graphene devices. (a) Hall bar structure on SiO2 with 10 contacts. (b) Hall bar structure on hBN with 8 contacts. The scale bar is 5 μm in both images...... 50

Figure 2.12 Schematics of capacitor structures. (a) Traditional parallel-plate capacitor. (b)

Au/hBN/graphene capacitor on hBN substrate sitting on Quartz...... 51

Figure 2.13 Two capacitor samples. (a) Au/hBN/graphene capacitor sitting on MoS2. (b)

Au/hBN/graphene sitting on hBN. The light red area is graphene underneath while the light-blue area illustrates the dielectric hBN. MoS2 shows a similar flat surface as hBN which is talked in detail in

Chapter 4...... 51

Figure 2.14 Sample platform...... 52

Figure 2.15 Helium-3 rotating probe diagrams. (a) Top part of the insert, composed with step motor,

Helium-3 dump and extendable airlock. (b) Bottom part of the insert with the main sorption, mini sorption pump and the sample platform...... 53

Figure 2.16 (a) Scheme of a 4-terminal resistance measurement with SR830 Lock-in amplifier. (b)

Diagram of a resistive measurement for resistance larger than a few hundred kΩ with SR830 Lock-in amplifier...... 54

Figure 2.17 Transport properties of Gr/hBN Hall bar structure (a), (b) Longitudinal resistivity and

Hall resistivity as a function of gate voltage for a typical Gr/hBN Hall bar device. (c), (d)

Longitudinal resistivity and Hall resistivity as a function of concentration in moiré superlattice Hall bar structure...... 55

Figure 2.18 The scheme of capacitor bridge in ANDEEN-HAGERLING 2700A/2500. Rs and Cs will get balanced with Co and Ro by the microprocessor. The resolution is 1fF with 10 mV excitation. ... 56

Figure 3.1 Schematics of our experiments...... 60

Figure 3.2 Quantum capacitance of graphene ...... 60

Figure 3.3 Graphene capacitors in quantizing fields...... 61

Figure 3.4 Many-body gaps through capacitance measurement ...... 62

Figure 4.1 Quality of hBN/graphene/hBN heterostructures fabricated by dry peel transfer...... 66

Figure 4.2 Graphene devices fabricated on a MoS2 substrate...... 67

Figure 4.3 Capacitance spectroscopy of WS2/graphene/hBN/Au...... 68

Figure 4.4 Capacitance spectroscopy of graphene on various atomically flat oxides at 2 K ...... 69

Figure 4.5 AFM topology and TEM cross section image of graphene on various substrates...... 70

Figure 5. 1 Transport properties of Dirac fermions in moiré superlattices...... 74

Figure 5. 2Quantization in graphene superlattices...... 74

Figure 5. 3Zak-type cloning of third-generation Dirac points ...... 75

Figure 6.1 Hofstadter butterfly in graphene superlattices...... 79

Figure 6.2 Capacitance spectroscopy of graphene superlattices...... 80

Figure 6.3 Magnetocapacitance oscillations and quantized density of states...... 81

Figure 6.4 Interactions in Hofstadter minibands...... 81

Figure 7. 1 Density and distance dependences for nonlocal valley currents...... 86

Figure 7. 2 Detection of long-range valley transport due to topological currents...... 87

PREAMBLE

2D materials have already attracted a tremendous amount of research in the past few years. Last year at the APS March Conference, there were more than four speeches at the same time over the four days, not to mention thousands of new papers and patents every year. This thesis modestly contributes to the quickly growing field focusing on the transport properties of a few novel vdW heterostructures.

Chapter 1 summarizes the main properties of 2D materials and their basic transport properties, paying close attention to graphene, hBN and MoS2. Based on these 2D materials, vdW heterostructures including vertical devices and graphene/hBN superlattices are presented.

Chapter 2 introduces the procedure of fabricating high mobility vdW heterostructures, in particular about graphene-based Hall bars and graphene-based capacitors. Meanwhile, the experimental setup and fundamental measurement methods are presented.

Chapter 3 utilizes capacitance measurements to study the behaviour of the density of states at zero and high magnetic fields in large-area high-quality graphene capacitors structure. Clear renormalization of the linear spectrum due to electron–electron interactions in zero fields and lifting of the 4-fold degeneracy Landau levels at high magnetic field are observed.

Chapter 4 focuses on the use of various layered materials as atomically flat substrates for making graphene-based vdW heterostructures. Graphene on molybdenum or tungsten disulphides and hBN are found to exhibit consistently high carrier mobility around 60 000 cm2/Vs. While on layered oxides such as mica, bismuth strontium calcium copper oxide, and vanadium pentoxide results in exceptionally low mobility of 1000 cm2 /Vs.

Chapter 5 studies high mobility Hall bar devices based on Graphene/hBN superlattices, where the periodic potential from the substrate mimics a moiré pattern leading to profound changes in

graphene’s electronic spectrum. Extra Dirac points appear as pronounced peaks in resistivity, accompanied with the change in the sign of the Hall signal.

Chapter 6 employs quantum capacitance measurement to examine the electronic spectrum of the

Graphene/hBN superlattices, where numerous replicas of the original Dirac spectrum appear at high fields and the suppression of quantum Hall ferromagnetism is observed.

Chapter 7 studies valley currents in the graphene/hBN superlattice structure by nonlocal measurement.

In graphene superlattices with broken inversion symmetry, topological currents originating from graphene’s two valleys are flowing in opposite directions to produce long-range charge neutral flow.

Part I Introduction

Chapter 1 Introduction to van der Waals heterostructures

VdW heterostructures are a new research area based on the development of different 2D materials, and therefore the study of the layered 2D materials plays a very important part for further construction[1-4].

In this Chapter, the 2D crystals family lead by graphene, hBN and 2D chalcogenides are introduced at the beginning, together with some basic electronic and magneto transport properties. Then novel vdW heterostructures constructed by different 2D materials will be introduced, in particular the vertical vdW heterostructures devices and the graphene/hBN superlattice based structure.

1.1 Introduction to 2D materials

Since graphene, the first 2D material, was first isolated in 2004 by Andre Geim and Konstantin

Novoselov [3, 5-12], more than a dozen different 2D materials have been isolated and studied, including hBN [13-17], black Phosphorous [18-21], 2D chalcogenides [22-42], 2D oxides [3, 43-54] and more. Those 2D materials have shown very interesting physical properties different from their bulk structure [3]. In this part, a brief introduction to a few members of the 2D family and their basic transport properties will be given.

1.11 Graphene

Graphene has a lot of exciting properties making it suitable for a broad range of applications in science and technology. In particular it is the ideal 2D electron gas for physics research [12], a highly efficient thermal and electrical conductor [55-59], has high stuffiness [60], very good optical transparency[61-66], shows ballistic transport of charge and large quantum oscillations [67-69], and a huge mobility up to 1,000,000 cm2/Vs [70]. Even more interesting is that graphene flakes can be produced easily by simply isolating from graphite, and graphene is also able to reform into fullerene, nanotubes and graphite by rolling and layering (as shown in Figure 1.1).

Figure 1.1 Carbon allotropes including 0D Fullerene, 1D Carbon Nanotube, 2D graphene and 3D

Graphite.

1.111 Band structure

The schematic structure of Graphene in the form of a hexagonal lattice is shown in Figure1.2a [71], where A and B are two equivalent sublattices in each elementary cell, where atoms from sublattice A is surrounded by three from sublattice B, and vice versa. The lattice vectors

푎 푎 a⃑ = (3, √3) , and a⃑ = (3, −√3) (1.1) 1 2 2 2

Where a is the distance between nearest-neighbour bonding which is 1.42 Å. The graphene lattice vector length |a⃑ 1| = |a⃑ 2| = 1.42 × √3 = 2.46 Å and the distance between two layers of graphene with AB stacking is 0.34nm.

Within the hexagonal lattice, carbon bonds are covalently bonded with sp2 hybridisation [72]. In the excited state of the electronic configuration of Carbon, there are four equivalent quantum mechanical

2 states: |2s>, |2px>, |2py> and |2pz>. In the case of sp hybridisation, |2s> is super positioned with |2px>

o and |2py>, making three orbitals arranged in the xy-plane with mutual angles of 120 (or π bonding) and leaving the unhybridised |2pz> (or π electrons) perpendicular to xy-plane. And it is π electrons that play the essential role in the unique performance of graphene.

Figure 1.2 (a) A honeycomb lattice with subblattices A and B shown in black and grey. (b) Reciprocal lattice vectors and some special points in the Brillouin zone. (adapted from reference [73] )

The first Brillouin zone of graphene with two different K points is illustrated in Figure 1.2b, where the unit reciprocal vector

2휋 2휋 푏⃑ = (1, √3), and 푏⃑ = (1, −√3) (1.2) 1 3푎 2 3푎

And the K and K’ vectors from the centre of the first Brillouin zone :

1 1 1 1 K = b ( , ), and K′ = b ( , ) (1.3) 2 2√3 2 2√3

Figure 1.3 The Electron energy spectrum of graphene. Right: Zoom-in of the electronic structure at the K point. (Adapted from reference [72])

The theoretical model for the electronic structure of graphene, the tight-binding model, was calculated in 1947 by P. R. Wallace[71]. With the tight-binding model based on the orbital wave function of the atoms, we are able to get the lattice wave function with Bravais vectors and can check how the wave function affect the changing energy as a function of the momentum k in the reciprocal lattice. In this tight-binding model only π electrons are considered. The onsite energy is omitted because the atoms are the entire same electronic configuration. Besides, π electrons are not considered to hop within the

A and B sublattice, but only between the nearest neighbour and second nearest neighbour atoms. For each sublattice, there are three nearest neighbours corresponding to the two K points in the reciprocal lattice of graphene, leading to two-fold valley and two-fold spin degeneracy in the electronic states of graphene. From the tight-binding model we can get the energy dispersion [71]

′ 퐸±(풌) = ± 훾√3 + 푓(풌) + 훾 푓(풌) (1.4)

Where

√3 3 푓(풌) = 2 cos(√3푘 푎) + 4 cos ( 푘 푎) cos( 푘 푎) (1.5) 푦 2 푦 2 푥

Where k is the electrons momentum; kx and ky are two components of k; 훾 is the electron hopping energy of the nearest neighbour atoms and 훾′ is the electron hopping energy to the second nearest neighbour atoms.

The energy dispersion, shown in Figure 1.3, has 훾 of 2.7 eV and 훾′ of 0.54eV. The energy spectrum includes two bands, the conduction band on the top and the valance band at the bottom. The Fermi level sits at the crossing points (Dirac Points) where those two bands meet and the energy is zero. We know that the second part in Eq.(1.4) would break the electron-hole symmetry and shift the conical point. However, 훾′ is negligible at low densities. This results in symmetric and linear electron-hole energy dispersion close to the Dirac points. The energy dispersion close to Dirac point can be described by

퐸±(풒) ≈ ±푣퐹|푞| (1.6)

Where q is the momentum relative to the Dirac points, vF is the Fermi velocity approximately

1×106m/s [71]. When 훾′ is not negligible, the energy dispersion is

9훾′ 3훾 퐸 (풌) ≈ 3훾′ ± 푣 |푞| − ( 푎2 ± 푎2푠𝑖푛3휃) |푞|2 (1.7) ± 퐹 4 8

푞 Where 휃 = tan−1( 푥) is the angle in momentum space. Hence, it’s clear that 훾′ breaks the electron- 푞푦 hole symmetry.

Based on the energy dispersion, graphene shows a zero gap between the conduction and valence bands which limits its application. However, people have now found many ways to open the gap between the two bands, such as using strain [74], bilayer graphene [75], nanoribbon graphene [76, 77], making defects on top [78-80], creating a superlattice [81-86] and so on. Those researches pave the way for the graphene applications in the future.

1.112 Electronic transport and the field effect

Owing to the gapless energy spectrum, graphene has shown very different transport properties from most conventional materials. And the most outstanding one is the ambipolar field effect [5]. For undoped graphene, the Fermi level stays at zero energy which would show zero density of states and accordingly an infinite resistivity. Due to the linear energy spectrum, graphene shows electron-hole symmetric transport behaviour. Transport measurement are made on a typical graphene-based Hall bar structure illustrated in Figure 1.4a, where graphene is placed on top of SiO2, Au is used as the contacts and the back gate voltage is applied through the bottom Si substrate. Details of fabrication procedure will be introduced in the Chapter 2.

By changing the gate voltage 푉푔, the charge carrier density 푛 can be tuned with

푛 = 휀휀0 × 푉푔/푡푒 (1.8)

Where t is the thickness of the SiO2, e is the electron charge and 휀휀0 is the permittivity of SiO2. When the density is changed by gating, the Fermi level will also move up and down, as shown in the inset of

Figure 1.4b. While at the Dirac point, the resistivity 𝜌 shown in Figure 1.4 is not an infinite value, because of the inhomogeneity and thermally smearing of the Fermi-function.

(Adapted from reference [87])

Mobility is an important parameter which illustrates how quickly the carriers can move through the graphene. From the resistivity curve, field-effect mobility 휇퐹퐸 can be extracted with 휇퐹 = 1/푒푛𝜌.

However, we can only trust this value away from the Dirac Point where the carrier concentration can be precisely tuned. Previous work has found that the impurity scattering and scattering from the surface roughness of the substrate are the main factor limiting the mobility [88-91]. In the past few years, different substrates and fabrication technologies have been developed to increase the mobility.

In particular, by encapsulating graphene between top and bottom hBN and making edge contacts for graphene contacts, the mobility can reach 1,000,000 cm2/Vs [70], shown in Figure 1.5.

Figure 1.5 (a) Schematic of high mobility sample with 1D contact. (b) Four-terminal resistivity measured from a 15μm × 15μm device fabricated by the vdW assembly technique with edge-contacts.

Low-temperature response is shown in the right inset. A negative resistance is observed, indicating ballistic transport. (Adapted from reference [70])

1.113 Magneto impedance and Quantum Hall Effect

When we changed Fermi energy within the Landau levels in high magnetic fields, the overall conductance will get quantized with value 퐺 = 푣푒2/ℎ, where h is the Plank constant, v is the integer filling factor. The reason is that the electrons in the 2D system travel only along the edges in the quantum Hall regime, shown in Figure 1.6.

Figure 1.6 In the quantum Hall regime, electrons travel through the edge only.

For graphene, due to two inequivalent Dirac valleys in the energy spectrum, the energy levels should have 4 times degeneracy: two actual spins of the electron and two valleys. The Landau levels spectrum energy of graphene is written as [72]:

2 퐸푁 = 푠푔푛(푁)√2푒ħ푣퐹|푁|, 푁 = 0, ±1, ±2 ⋯ (1.9)

Where ħ is the reduced Plank constant and N is the number of Landau level. N=0 relates to the zero

Landau level at Dirac point. From equation (1.9), it is clear that the levels are not equally spaced and the neutral point has an associated LL.

Experimentally, the quantum Hall effect (QHE) in graphene was firstly observed in 2005 [12], illustrated in Figure 1.7. Where the observed quantized plateaus for Hall conductance are at ve2/h with filling factors v=±2, ±6, ±10…, which is very different from conventional plateaus, but consistent with the four times degeneracy. Besides, the plateau is not available at 0LL but with perfect symmetry between electron and hole states, which is in agreement with equation (1.9).

Figure 1.7 Integer quantum Hall effect in graphene. ρxx and σxy as a function of the carrier density n at

14T. (Adapted from reference [12])

With high quality samples, the integer filling factors can be observed. As shown in Figure 1.8b, besides the strong incompressible behaviour that occurs at v=4(N+1/2), clear incompressible states at intermediate integer filling factors v= 0, ±1, ±3, ±4, ±5 are also impressive, proving the fully lifting of four-fold degeneracy per LL. The reason for lifting of the degeneracy is attributed to the enhancement of Coulomb and exchange interactions in the sample.

The most interesting point is the many-body interactions resulting in the fractional quantum Hall effect (FQHE) [6, 17, 92-94], where the Hall plateaus will be situated at fractional values of the filling factor. As illustrated in Figure 1.8c, fractional filling factors are also visible at

1 2 3 4 3 2 4 10 14 8 푣 = ± , ± , ± , ± , ± , ± , ± , ± , ± , ± , … … (1.10) 3 5 7 7 5 3 3 7 9 5

For filling factors v < 1, the sequence follows the typical composite fermion sequence. While for larger fractional filling factors, the system condenses into incompressible states only at 4/3, 8/5, 10/7,

14/9 [93].

Figure 1.8 High mobility suspend graphene is studied focusing on the many body effect at high magnetic field, showing integer QHE and FQHE. (a) The scanning single electron transistor (SET) is

1.12 Hexagonal boron nitride (hBN)

hBN, different from its allotropes of sphalerite boron nitride (sBN) and wurtzite boron nitride (wBN), is very interesting in its stable crystalline form with a layered structure and the atomically flat surface

[95, 96], as shown in Figure 1.9(a). Similar to graphene, it has a hexagonal structure with two sublattices and strong covalent bounds [97]. With exfoliation method to annihilate the van der Waal

force between layers, we can get hBN flakes down to monolayers (illustrated in Figure 1.9(b)). The lattice constant of hBN is 2.52 Å with AA’ stacking order, the distance between the closest nitride and boron is 1.445Å, and between two layers is about 3.33Å.

Figure 1.9 (a) Schematic of hBN structures. (b) hBN flake prepared by mechanical exfoliation,

Different layers of hBN could be noticed from monolayer to bulk, the scale bar is 20um.

Different from graphene, hBN is an insulator with an energy band gap of ~6eV, providing great potential as a substrate and encapsulating layer[98]. Figure 1.10b shows the AFM image of the roughness for hBN, graphene and SiO2, where hBN is as flat as graphene and three times less rough than SiO2 [99]. The atomically smooth surface is free of dangling bonds and charge traps, making hBN an ideal substrate and protective film. As introduced previously, these essential properties have paved the way to mobility up to 1,000,000 cm2/Vs as illustrated in Figure 1.5, which is 100 times better than on SiO2 substrate.

Figure 1.10 (a) AFM image of monolayer graphene on hBN with electrical leads. White dashed lines indicate the edge of the graphene flake. Scale bar, 2 µm. (b) Histogram of the height distribution

(surface roughness) measured by AFM for SiO2 (black triangles), h-BN (red circles) and graphene-on-

hBN is also an excellent dielectric material, which can be used in field-effect transistors for a top gate or as a barrier layer in tunnelling transistors [14, 100, 101]. For a typical tunnelling transistor with hBN as the tunnelling barrier, the switch ratio of the tunnelling transistor is up to 104 at room temperature (shown in Figure 1.11a), and the tunnelling current shows an exponential dependence at higher bias voltages. While at low bias voltage, the tunnelling resistance increase exponentially with the number of the hBN layers in the barrier as illustrated in Figure 1.11b.

1.13 Transition metal dichalcogenides

Another appealing group of 2D materials is the transition metal chalcogenides (TMDCs), which have the structure of MX2, where M is a transition element and X is related to the chalcogen atoms S, Se,

Te, etc. In contrast to the zero-band gap linear dispersion in graphene and insulating hBN, TMDCs are semi-conducting with electron properties resembling more conventional semi-conductors.

However, compared to conventional silicon/III-V materials, these layered materials have shown fascinating electrical, optical and mechanical properties with the tunable band gaps [27, 29, 32, 35, 36,

102-111]. WS2, MoS2, MoSe2, WSe2, NbSe2 and TaS2 are amongst the most popularly studied materials due to the available crystals from the natural mining. In particular, W compounds show a stronger spin-orbit effect than Mo, while Se compounds are more reactive than S [3, 40]. The most popular MX2 is the layered 2H-MoS2 with a high mobility, a thickness-dependent band gap (indirect band gap for multilayers (1.2eV) and a direct band gap for monolayer (1.8eV)) [112], showing potential application in electronics and particularly optoelectronics. Besides, MoS2 has shown novel

physics as coupled spin-valley effect and Valley Hall effect, leading to the development of a new niche field of research, valleytronics [3, 27, 38, 113, 114].

Shown in Figure 1.12a, a layer of MoS2 is constructed of two layers of S with a layer of Mo in- between and connected with covalent bonds. The crystal lattice constant is 3.2 Å and the distance between two layers is 6.5 Å. With the usual mechanical exfoliation method, we are able to isolate different layers of MoS2 flakes down to monolayer (illustrated in Figure 1.12b).

With a band gap within 1.2eV to 1.8eV, MoS2 can be used as the main channel to prepare in-plane field effect transistors. The typical behaviour for a monolayer MoS2 transistor is shown in Figure

1.13a with an on-off ratio up to 108 [23]. Also, using highly doped graphene contacts [115],

Shubnikov–de Haas oscillations in MoS2 can be observed and the degeneracy of monolayer MoS2 is between 2 to 4, which may be due to the split energy bands.

2 MoS2 device with graphene contacts. The mobility for monolayer MoS2 is around 1000 cm /Vs.

(Adapted from reference [115])

1.14 Other 2D materials

Meanwhile, people have discovered a vast variety of other 2D materials (classified in figure 1.13), including the Graphene family, other 2D chalcogenides and 2D oxides. In graphene derivatives, fluorographene is a fluorocarbon derivative of graphene with sp3 hybridized structure, making it a highly insulating barrier [116-118]. Graphene oxide, composed with oxygen and hydrogen in variable ratios, is widely used in coatings, water purification and battery electrodes [119-127].

Many other 2D chalcogenides have been isolated from their layered structure down to monolayer, but the research has been limited due to either the shortage in crystals or the instability in the air. The same problem is restricting the study of some 2D oxides, such as BSCCO and TiO2 [3]. To overcome the problems of instability, these materials need to be protected from the ambient environment with some fabrication techniques, which involve preparing samples in an inert gas, encapsulation with hBN or in-situ preparation and characterisation (in one cryostat). In particular, Da et al have prepared monolayer BSCCO flakes with graphene encapsulation[128], showing that monolayer BSCCO is a high Tc superconducting material, Figure 1.15a. In our work, graphene or thin hBN is used to encapsulate NbSe2 of different number of layers. This work has shown that NbSe2 remains superconducting down to monolayer, illustrated in Figure 1.16b and c.

Figure 1.15 (a) R–T curves for graphene/BISCCO vdW heterostructures measured at applied bias currents of Idc=0, 0.04, 0.08, 0.16, 0.20, 0.24, 0.28, 0.32 and 0.36 mA, showing a Tc around 88K. Inset: the schematic of the sample and transport measurement, where BISCCO is encapsulated with graphene and Au contacts is on top of the graphene, bringing the non-zero value of resistance below

88K. (Adapted from [128]) (b) Schematics of our NbSe2 sample, where NbSe2 is placed on hBN and covered with thin hBN. Bottom left is a cross sectional bright field STEM image of a bulk hBN/bilayer NbSe2/bulk hBN with the extracted interlayer distances on the right. Centre –

Superimposed STEM-EELS image with elemental profiles for the niobium–M4, 5 edge (orange) and selenium-L3 edge (green). (c) Tc of NbSe2 changes with thickness. The dotted line in the inset is a guide to the eye.

1.2 VdW heterostructures

Amongst the research of 2D materials, vdW heterostructures, which is to make novel structures by stacking different 2D crystals on top of each other (illustrated in Figure 1.16), has opened up a new research direction for exploring novel physics. These structures have been coined as artifical atomic- scale Legos and have shown many new physics phenomena and device functionality [3]. In this work, vertical heterostructure (Graphene/hBN/Au, Graphene/hBN/Graphene) and Graphene/hBN superlattices have established revolutionary properties and are going to be introduced in the following.

Figure 1.16 Building vdW heterostructures.

1.21 Vertical heterostructures

The novel vertical vdW heterostructures include the tunneling transistors, capacitors and double-layer structures. For the tunneling transistor, MoS2, hBN and WS2 have been used as a tunnel barrier and graphene is used as one or both of the electrodes [14, 100, 101, 129]. An example of a tunneling device is shown in Figure 1.17, where graphene is used as the electrodes and hBN is used as the

tunneling barrier. The tunneling current can be controlled by changing the Fermi energy of the electrode through the gate voltage [101], which effectively tunes the height of the tunneling the barrier. Capacitor structures have shown the advantage in detecting the DoS when the Fermi level is changed in the graphene electrode (details will be shown in Chapter 3). For double-layered structures, two independent graphene layers are spatially separated by a thin insulating barrier. When the spacer layer is sufficiently thin, electron-electron interactions between two separated 2D systems can be observed for example in Coulomb drag experiments. Illustrated in Figure 1.18, two layers of graphene with a tri-layer hBN spacer can still show significant inter-layer Coulomb interactions by drag resistivity [3, 130].

Figure 1.17 (a) Schematic of a tunnelling transistor device. Top hBN is the encapsulation layer; bottom hBN is used as the substrate and the middle hBN functions as a tunnel barrier. (b) I-Vs for different Vg (in 10V steps). (Adapted from reference [101])

1.22 Graphene/hBN superlattice

Before talking about the superlattices, Hofstadter's butterfly should be introduced, which was predicted by Douglas Hofstadter in 1976 [131]. The Hofstadter’s butterfly is theorised behaviour of

2D electrons gas when they are subjected to a magnetic field at the cyclotron frequency and to the periodic electric potential in the 2D lattice at a quantized frequency. Before the outcome of graphene/hBN superlattices, experimental confirmation of the theory was not possible because of the difficulty in making fine structures.

Figure 1.19 Hofstadter’s butterfly. (Theory behaviour of electrons in 2D lattice at a filed. x-axis is the flux quantum, y-axis is the energy).

Graphene/hBN superlattice is based on crystallographic alignment between graphene and hBN, because they have a similar honeycomb structure and only a 1.8% lattice difference. When we are making a ‘Lego’ by stacking thin graphene on an atomically flat boron nitride substrate with a certain angle, a moiré pattern with different periodicity comes into being, as shown in Figure 1.19. The moiré pattern provides an additional periodic potential to graphene, which results in additional Dirac cones at high charge density. When a magnetic field is applied to the 2D electron gas in graphene, the energy diagram known as the Hofstadter butterfly appears [84, 85, 132-136]. In order to search for the

Hofstadter butterfly in this graphene/hBN superlattices, both resistive and capacitive devices are fabricated and investigated (Details will be shown in Chapter 4 and 5).

The band structure in the Gr/hBN superlattice structure is very complicated, specifically whether a gap opens up in the neutrality point for the graphene. Ponomarenko et al. first reported zero gap in the transport measurement (shown in Figure 1.21a) [134]. However, B. Hunt et al. and C. R. Dean et al. observed the gap up to 600K and saw it decreasing with reducing the periodicity of the superlattice potential (shown in Figure 1.21b and c) [85, 137]. In our recent papers, the gap was present for non- encapsulated device, but disappeared for encapsulated samples (shown in Figure 1.21d and e). This was attributed to the difference of a commensurate and incommensurate state of the superlattice [132,

138]. Recently by checking the valley Hall effect at zero magnetic field, we found topological current available in both encapsulated and nonencapsulated devices (Details in Chapter 7), which suggests the presence of a band gap since the prerequisite condition for a valley current is to have the broken

inversion symmetry[86]. We explain this experimental discrepancy by two routes. The first one is that inhomogeneity results in many electron and hole puddles, some n-doped and p-doped. When we change the Fermi energy by gate tuning, the small gaps will be covered by this the fluctuation [139,

140]. Another possible explanation is the edge states that short the gap. However, the precise origin of the gap in the superlattice is still uncertain [74, 141], which needs further experimental and theoretical studies to resolve the issue.

Figure 1.21 The gap issue at the neutrality point. (a) Temperature dependence of the minimum conductivity at the main and secondary NPs show no-gap behaviour. The electron-side NP is scaled

by a factor of 20. (Adapted from reference [134]) (b) Gaps measured by thermal activation at the CNP and hole satellite peak positions with 4 different devices. (Adapted from reference [137]) (c)

Correlation of observed band gaps with moiré wavelength λ. (Adapted from reference [85]) (d)

Chapter 2 Fabrication of vdW heterostructure based devices and experimental setup

In this chapter, firstly, the fabrication of vdW heterostructure based devices is presented, including flake preparation, the technique for stacking flakes to construct the heterostructures and photolithography procedures. Two types of samples that are present throughout all the research in the thesis are shown in detail: graphene-based Hall bars, and graphene-based capacitors. Then the experimental setup for transport measurements are shown, with emphasise on the Helium-3 rotating insert for low temperature measurements. Finally, the measurement methods for Hall bar structures and capacitors are introduced separately.

2.1 Preparing flakes

To fabricate vdW heterostructure samples, preparing flakes with different layers on target substrates is the very first step. To get ideal flakes from different crystals, both mechanical exfoliation and

Chemical Vapor Deposition (CVD) method can be utilized. Mechanical exfoliation provides flakes with better quality while the CVD method can produce larger flakes. For substrates, SiO2/Si wafers and PMMA/PMGI resists are mostly used. A SiO2/Si substrate provides better optical contrast for the flakes and a convenient path to apply gate voltage through Si layer. While PMMA/PMGI resists are more convenient and efficient for the transfer process.

2.11 Mechanical exfoliation

The mechanical exfoliation method is based on micromechanical cleavage of bulk flake crystals to graphene. To prepare graphene onto the SiO2/Si substrates or PMMA/PMGI resists, we exfoliate thin graphite flakes with scotch tape first, and then stick the flake to the substrates with the scotch tape.

After suitable force for enhancing attachment between the flake and substrates, the tape will be peeled off and leave graphite with different thicknesses on top of the target down to one atomic layer. The lateral size of the flakes can be as large as a millimetre when using clean and flat graphite with less defects and impurities. The same procedure is used for preparing hBN flakes. In Figure 2.1, graphene and hBN flakes, produced by mechanic exfoliation, are shown on both SiO2/Si and PMMA/PMGI substrates. Different background colours are a result of the filters with different wavelengths which is used to increase the contrast of the flake relative to the substrate and each other.

2.12 CVD method

Compared with liquid-phase exfoliation of graphite [142] and epitaxial growth on silicon carbide

[143], graphene growth with CVD method on Cu substrates is the most accessible approach to obtain graphene with modest quality and large size for industry application. Until recent, the size of graphene grown on copper foil has reached 30 inches but the mobility is relatively low (7,350 cm2V-1s-1 at 6K

[62]), this is due to the defects of CVD graphene with small grain size, abundant grain boundaries

[144], mechanical defects (e.g. hole, crack, and wrinkle) [145], impurities [146], etc.

Figure 2.2 CVD system for graphene production.

Graphene is prepared through the CVD System (shown in Figure 2.2), usually composed of a controlling system, three gas injections (H2, Ar and CH4), a furnace, a quartz tube and a pump. After inserting the copper foil into the quartz tube, the system is heated to 1,000 oC with 10 cubic centimetres per minute (sccm) flow rate of H2 at 80 mtorr for 20 minutes to pre-treat the copper foil to get a cleaner surface. Then, together with H2, a flow of 40 sccm of CH4 will be provided at 400~700 mtorr for 30 min for the graphene growth on the copper. After cooling down, graphene would be shown on both sides of the copper foil.

Figure 2.3 CVD graphene. (a) CVD Graphene on SiO2. (b) CVD graphene on PMMA.

2.2 VdW heterostructure device fabrication

As described by Professor Geim, making VdW heterostructures is ‘more like playing a Lego game’[3], which is to assemble different flakes together in a chosen sequence to make a new artificial structure.

To fabricate heterostructures devices, the first step is to prepare the flakes and stack them layer by layer to construct vdW heterostructures as designed, which requires different transfer technologies.

To make the attachment better and the interface cleaner, suitable annealing procedure should be used.

Then, lithographic process is used for the contacts and Mesa fabrication.

2.2.1 Making vdW heterostructures

The key point for making vdW heterostructures is to stack the layers together with as little contamination as possible. In practice, there are two basic transfer technologies mainly used in the transfer process.

‘Wet’ transfer method

‘Wet’ transfer is a method which will get the flake wet during the fabrication. The idea is to exfoliate the flake on the substrate with polymer, and then dip them in some solvent, which dissolves the substrate but floating the polymer with flake. Take graphene on SiO2/Si substrate as an example,

PMMA is spun on top of the substrate. After this a tape with window is attached to PMMA with graphene flake in the middle of the window. Then, 3% KOH is used to dissolve the substrate, leaving the PMMA and tape floating on top of KOH. Finally, the system is transferred to DI water to clean and be ready for next step. The whole process is illustrated in Figure 2.4.

Figure 2.4 ‘Wet’ transfer. (a) Graphene is placed on top of SiO2 by mechanical exfoliation. (b)

For CVD graphene, we need a different solvent because CVD graphene is grown on a Cu substrate.

The first step is to cover one surface of the copper with a thin film of (PMMA). Then, oxygen plasma is used to etch away the graphene on the other side of the copper foil. And then, the sample is placed in aqueous ammonium persulphate ((NH4)2S2O8) solution to dissolve the copper layer [62]. This etching will leave a PMMA membrane with the CVD graphene floating on the surface of the solution.

‘Dry’ transfer method

‘Dry’ transfer is another technology which can prevent the flake from solution contamination and leaves a far cleaner flake than ‘Wet’ transfer. The idea is to spin two different layers of polymer on top of the substrate first and then exfoliate flakes onto the polymer surface. After dissolving the bottom polymer, the flake with top polymer would get floated and ready for transfer. In practice,

PMGI and PMMA are spun onto a wafer with PMGI at the bottom, and then the graphene flake is exfoliated on top of PMMA. Finally, the bottom PMGI can be dissolved by injecting MF-319, leaving the PMMA and the flake floating on top. The schematic process is shown in Figure 2.5.

After preparing different flakes on top of PMMA with either ‘Dry’ or ‘Wet’ transfer method, we can start to transfer one flake to another. The method is to set the flakes face to face, and then gradually attach to each other, shown in Figure 2.6. The final step is to remove the top PMMA either by dissolving in acetone or by peeling off. Dissolving in acetone brings the same problem as ‘Wet’ transfer method, while peeling off can provide clean heterostructures with high quality but may also lead to a scrolled edges due to tension.

Figure 2.6 Transfer processes after preparing flakes on PMMA. (a) Turn the flake to face the target area. (b) Attach the flake to the target flake gradually. (c) Remove the top PMMA.

2.2.2 Superlattice alignment

To prepare van der Waal heterostructures with a moiré superlattice, an extra procedure for the transfer process is needed, which is to make an alignment during the transfer process. The idea is to distinguish the crystal orientation first for both flakes and then to adjust the orientation before assembling.

The orientation of the flake can be determined mainly through the edges of the flakes. However, hexagonal structures have two types of edges with a relative angle of 30o difference: zigzag and armchairs, illustrated in Figure 2.7a. Usually, it’s hard to distinguish between them, without more complicated techniques, which leave only a 50% chance of proper alignment. A typical hBN flake is shown in Figure 2.7.b, where two types of edges can be clearly observed. After graphene is aligned to the hBN (shown in Figure 2.8a), we can see one of the edges of graphene matches one edge of hBN, and a beautiful moiré pattern with a superlattice constant of 12nm is measured by AFM (shown in

Figure 2.8b).

2.2.3 Annealing process

After the transfer procedure, the heterostructure is annealed to improve the interface adhesion between the flakes and to remove any hydrocarbon and PMMA residue. Here we use 90% Ar and 10%

o H2 with three steps. The first one is to set annealing Temperature to 100 C to remove the water molecule on the heterostructure, and then we set it to 200oC to get rid of hydrocarbon. Finally, we increase the temperature to 300 oC to anneal the sample.

2.2.4 Lithography process

After assembling clean heterostructures, photolithography or electron-beam lithography can be used for patterning the device design and contacts. E-beam lithography has better resolution where nanometer size devices < 10nm can be fabricated but low in efficiency. Photolithography is much faster but has a lower resolution of ~500 nm. The idea of photolithography is to cover the device with optical resist, then to use light to expose the area where you want to remove, and then a pattern will be obtained after removing the exposed area by developer.

Figure 2.9 The schematic procedure for device fabrication with photolithography. (a) Photoresist coating with a bi-layer photoresist: PMGI and S-1805. (b) Exposure of the pattern with the

LaserWriter. Photolithography uses photoresist with ultraviolet light. (c) Development after the exposure. (d) Deposition the metals for the contacts. (e) Lift-off procedure. (f) Etching Mesa with

Plasma.

Photoresists coating, exposure and development

To fabricate an undercut structure, a bi-layer photoresist configuration is used for the photolithography, made of a bottom polydimethyl glutarimide (PMGI; Microchem Corp) and a top layer of Microsposit S-1805, in which S-1805 is sensitive to UV exposure while PMGI can be easily dissolved by the developer. To get a good adhesion between the substrate and the graphene, we prebake the device at 170oC for 10 minutes to remove water molecules from the substrate surface.

Then PMGI is spin coated at 4,000 rpm and baked at 170oC for 5 minutes afterwards. Then, the same spin rate is used for coating of S-1805 with a baking temperature of 110oC for 1 minute. To increase the adhesion of the resist, hexamethyldisilazan (HMDS) may be added to the recipe before spinning the photoresists.

Microtech LW405 laser writer with 530 nm laser is used for the exposure. A dose test should always be done to decide the proper dose for the undercut exposure. After the exposure, the sample is dipped in 2.45 wt % TMAH solutions (MF-319 developer) for 1 minute to get the pattern, then is washed in

DI water for 3 minutes to clean the device. The sample is then dried with nitrogen gas and checked under the optical microscope with 620 nm filter.

Deposition

After making the pattern, a Moorfield Minilab system e-beam evaporator is used for the metal deposition. In this system, high voltage electron beams (10kV) are used to vaporize the metal for deposition under high vacuum. Chromium (Cr) is used as an adhesion metal and gold (Au) is used as the contact metal. A 5-nm thick layer of Cr and 40-nm Au is deposited then at a rate of 1.2 Å/s. The rate is measured by a quartz crystal sensor and the thickness of the deposition is calculated by a

DekTak Stylus Profiler.

Lift-off

After metal deposition, we need to remove the metal film on top of PMGI/S-1805 photoresist by dissolving in acetone and MF-319. The sample in submerged in acetone first for sufficient time to lift- off the S-1805 and metals, then the sample is placed in fresh acetone for 10 minutes for cleaning of any leftover S-1805. After that, the sample is dipped in in MF-319 for 1minute to remove the remaining PMGI layer and transferred to DI water and IPA for further cleaning.

Etching Mesa

To get specific structures of the sample, oxygen-plasma dry-etching may be used on the photolithography mask layer. Resist is used to protect the area that needs to remain, after etching the device for 2 minutes with the oxygen-plasma etcher, the sample is left in white light for 5 minutes for full exposure and then placed in acetone for 10 minutes with initial 30 seconds ultrasonic agitation to help dissolve the S-1805 layer which may be hardened during the plasma-etching treatment. Finally,

MF-319, DI water and IPA treatments are used to clean identical to the lift-off procedure.

2.2.5 Hall bar structure

The Hall bar geometry is a simple powerful design in checking electronic properties. Results obtained in Chapter 5 and 7 are all based on measurements made in the Hall bar geometries. A 2D Hall bar structure (shown in Figure 2.10a) can be recognized as a 2D channel with current passing in the x- direction. When a magnetic field B is applied in the z-direction, charged particles will move in the y- direction as well, due to the Lorentz force and create a Hall voltage VH. This voltage builds up until the equilibrium state is achieved,

푒푣퐵 = 푒퐸 (2.1)

Where e is the elementary charge; v is the drift velocity; Electric field 퐸 = 푉퐻/푤 and Hall voltage 푉퐻 = 퐼퐵/푛푒 . Within the Drude model, mobility µ and density n can be described by:

휎 휇 = = 1/𝜌 푛푒 (2.2) 푛푒 푥푥

푛 = 1/푒𝜌푥푦 (2.3)

Where Hall resistance 𝜌푥푦 = 푉퐻/𝑖; 𝜎 is the conductivity along the x-direction and 𝜌푥푦 is the Hall resistivity.

The schematic Hall bar structure for graphene device is shown in Figure 2.10b, where the top hBN is used to protect the device from contamination, and bottom hBN is used to reduce the scattering from the rough surface of SiO2. Two typical Hall bar devices are shown in Figure 2.11, where graphene

Hall bar structures are placed on SiO2 and on hBN substrate separately.

Figure 2.10 (a) The schematic of Hall bar structure. (b) Graphene-based Hall bar structure sits on top of hBN substrate and is encapsulated by hBN.

Figure 2.11 The optical images of fabricated graphene devices. (a) Hall bar structure on SiO2 with 10 contacts. (b) Hall bar structure on hBN with 8 contacts. The scale bar is 5 μm in both images.

2.2.6 Capacitive structure

The traditional capacitor is a parallel-plate structure with two metal conducting plates separated by a dielectric layer in the middle, shown in Figure 2.12a. When one plate of the capacitor is made with a material of low DoS such as graphene, a quantum capacitance CQ appears due to the large change of

DoS when changing density. Then the total capacitance can be described by

1 1 1 = + (2.4) 퐶 퐶퐺 퐶푄

2 Quantum capacitance CQ can be described by the DoS where CQ = Se × DoS, and the usual geometrical capacitance CG is calculated from the traditional parallel-plate model: 퐶퐺 = 휀휀푟푆/푑, where d is the thickness of the spacer, S is the common area between two plates and 휀휀푟 is the dielectric constant.

The schematic structure of the graphene-based capacitors is shown in Figure 2.12b, where Quartz is used to reduce the parasitic capacitance, and bottom hBN provides a flat bottom substrate to graphene.

A top gold layer and a graphene layer construct the two plates for the capacitor with hBN as the dielectric layer. Two typical capacitor samples are illustrated in Figure 2.13.

Figure 2.12 Schematics of capacitor structures. (a) Traditional parallel-plate capacitor. (b)

Au/hBN/graphene capacitor on hBN substrate placed on Quartz.

Figure 2.13 Two capacitor samples. (a) Au/hBN/graphene capacitor placed on MoS2. (b)

Chapter 4.

2.3 Measurement setup

Transport properties of the van der Waal heterostructure devices are measured in Helium Cryostats with a base temperature of 4.2K. By pumping Helium-4 and using Helium-3 inserts, the temperature can go down to 0.3K.

2.3.1 Helum-3 rotating probe

The sample is mounted within the chip carrier in the sample holder of a Helium-3 rotating probe before inserting into the Variable temperature insert (VTI) of the cryostat, as shown in Figure 2.14.

The Heluim-3 rotating probe can change temperatures in the range 0.3 to 300K with a rotating degree of 00 to 360o, shown in Figure 2.14.

Figure 2.14 Sample platform.

The Helium-3 insert functions by pumping in the liquefied Helum-3 after cooling down to Helium-4 temperature, which reduces the vapour pressure and hence the temperature. After the probe is inserted into the VTI of the cryostat, the cooling power of the VTI is used to cool down to 2.2K and to liquefy

Helium-3. The pumping and thermal isolation of liquefied Helium-3 is controlled by charcoal sorption pumps that are integrated within the probe. Helium-3 gas is contained in an isolated closed circuit at

approximately 2 mbar pressure and it allows continuous operation for up to 24 hours. The rotating part is based on a step motor, which is controlled by the Rotating Sample Probe Interface Unit.

Figure 2.15 Helium-3 rotating probe diagrams. (a) Top part of the insert, composed with step motor,

Helium-3 dump and extendable airlock. (b) Bottom part of the insert with the main sorption, mini sorption pump and the sample platform.

2.3.2 Resistive measurement

Resistance measurements are made with a SR830 Lock-in amplifier and the measurement circuits are presented in Figure 2.16. For measurement object less than a few hundred kΩ, a series resistor of

10MΩ is connected in the circuit to provide a constant AC current for the circuit, then the differential

Voltage drop between the two probes V1 can be measured and the resistance is determined, shown in

Figure 2.16(a). This is a 4-terminal measurement which removes voltage drop across the contacts and measurement wires. Figure 2.16(b) shows a 2-terminal measurement for resistance larger than a few

hundred kΩ, where the AC voltage is converted into current and the total resistance can be obtained by V/I.

Figure 2.16 (a) Scheme of a 4-terminal resistance measurement with SR830 Lock-in amplifier. (b)

Diagram of a resistive measurement for resistance larger than a few hundred kΩ with SR830 Lock-in amplifier.

Four terminal measurements are used in the transport measurement for the longitudinal (Rxx) and transversal resistance (Rxy). The transport behavior for the Hall bar structure device is shown in

Figure 2.12a, where a large peak in the longitudinal resistance is shown at the Dirac point, together with a reversal signal in the Hall voltage in Figure 2.12b. This is due to the minimum of concentration at Dirac point and Dirac fermions changing the sign when the Fermi levels passing the Dirac point.

For Hall bar structures patterned from aligned samples, the graphene/hBN superlattice, secondary

Dirac point appears together with a changing sign of Hall voltage due to the miniband, as shown in

Figure 2.12 c and d. Details will be shown in Chapter 6.

Figure 2.17 Transport properties of Gr/hBN Hall bar structure (a), (b) Longitudinal resistivity and

Hall resistivity as a function of gate voltage for a typical Gr/hBN Hall bar device. (c), (d)

Longitudinal resistivity and Hall resistivity as a function of concentration in moiré superlattice Hall bar structure.

2.33 Capacitive measurement

Capacitor Bridge ANDEEN-HAGERLING 2700A/2500 is used to measure capacitive structures. The idea for the bridge circuit, shown in Figure 2.18, is to select proper Co and Ro by the microprocessor to make a balance with the resistance Rs and capacitance Cs of the capacitor, based on the ratio of voltage V1 and V2. Where we have 푉1/푉2 = 푅표/푅푠, and 푉1/푉2 = 퐶푠/퐶표. V is the bias voltage which can shift the Fermi level of the graphene and DoS, accordingly, quantum capacitance and total capacitance will be changed.

Figure 2.18 The scheme of capacitor bridge in ANDEEN-HAGERLING 2700A/2500. Rs and Cs will get balanced with Co and Ro by the microprocessor. The resolution is 1fF with 10 mV excitation.

Transport measurements for graphene based capacitors are shown in Figure 2.19, where clear dips are observed at the Dirac point due to the minimum of DoS. What’s more, in Figure 2.19b, a second

Dirac point is observed in capacitance structures based on moiré superlattice in the heterostructures.

Details will be shown in Chapter 3 and Chapter 6.

Figure 2.19 (a) Total capacitance as a function of concentration in zero magnetic field for an

Au/BN/Gr capacitor structure. (b) Total capacitance for an Au/BN/Gr device in moiré superlattice capacitor structure

Part II Experimental results

Chapter 3 Interaction phenomena in graphene seen through quantum capacitance

My contribution

I have made some samples, performed all the transport measurement (not include high magnetic field over 18T), participated in analysing the data, fitting the curves with the model and preparation of the figures.

Chapter 4 Electronic properties of graphene encapsulated with different two-dimensional atomic crystals

My contribution

I have performed all the transport measurement, analysed the data and prepared all the transport figures.

Chapter 5 Cloning of Dirac fermions in graphene superlattices

My contribution

I have performed the transport measurements (not include high magnetic field over 18T), participated in analysing the data, fitting with the model and preparation of the figures.

Chapter 6 Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

My contribution

I have raised the idea, performed all the transport measurements (not include high magnetic field over

18T), participated in analysing the data and preparation of the figures.

Chapter 7 Detecting topological current in graphene superlattices

My contribution

I detected the topological current, performed all the transport measurements, analysed all the data and prepared all of the figures.

Chapter 8 Conclusion

This thesis has introduced and studied several novel VdW heterostuctures, focusing on the transport properties of graphene-based capacitors placed on different substrates and graphene/hBN superlattice based capacitors and Hall bar structures.

Capacitance measurement has shown its advantage in detecting the density of states and the spectrum of electrons. In Chapter 3, we used the capacitance measurements to study the properties of graphene, where we detected clear renormalization of the linear spectrum due to electron–electron interactions at zero magnetic field and lifted degeneracy in high magnetic field. In Chapter 4, we utilized capacitive measurement to probe the electronic spectrum of graphene on different substrates, finding that molybdenum or tungsten disulphides and hBN are able to serve as ideal substrate for graphene, while layered oxides such as mica, bismuth strontium calcium copper oxide, and vanadium pentoxide are with exceptionally low quality which is due to the absence of self-cleansing between graphene and oxide substrate. In Chapter 6, we again employed the capacitance measurement to study the electronic spectrum of Graphene/hBN superlattice, where we observed additional Dirac points at zero magnetic field and numerous replicas of the original Dirac spectrum at high fields. In addition, we found a suppression of quantum Hall ferromagnetism and additional ferromagnetism within replica spectra.

Besides the transport research with quantum capacitance measurement, classical Hall bar structures were also employed to study to properties of Graphene/hBN superlattices. In Chapter 5, second Dirac point appeared with pronounced peaks in resistivity, accompanied by reversal of the Hall signal in field. At strong field, Zak-type cloning of the third generation of Dirac points is observed as numerous neutrality points. In Chapter 7, valley current from graphene’s two valleys are detected with nonlocal measurement, meaning that the graphene superlattice is with the broken inversion symmetry.

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