Physics in 2D Materials

Taro WAKAMURA (Université Paris-Saclay)

Lecture 5 Today’s Topics Lecture 5 (final):h-BN/Black Phosphorus/Xene

5.1 hexagonal Boron-Nitride

5.2 Black Phosphorus

5.3 Xene Hexagonal boron nitride Hexagonal Boron-Nitride (h-BN) Hexagonal boron nitride (h-BN) as a substrate for

Hexagonal boron nitride Two dimensional van-der Waals insulator Easy to exfoliate (Large ~ 6 eV)

Atomically flat, less charge traps, small lattice mismatch with graphene Good candidate as a substrate for graphene! Hexagonal Boron-Nitride (h-BN) Disorders that reduce mobility also come from resist residues Graphene protected from external environment should have better mobility Graphene encapsulated by h-BNs Hexagonal boron-nitride (h-BN) is an ideal material as a substrate for graphene: flat, flee from charge inhomogeneity Graphene encapsulated from two h- BNs should be flee from resist residues, charged impurities.

L. Wang, Science 342, 614 (2013). Hexagonal Boron-Nitride (h-BN) Transport measurements of graphene on h-BN Moiré pattern is clearly observed by AFM images

Additional peaks are observed in Rxx Signature of the secondary Dirac points away from the original Dirac point

Sign changes of Rxy around the secondary Dirac points Switch between electron & hole nature of mass- less fermions around the secondary Dirac points

M. Yankowitz et al., Nat. Phys. 8, 382 (2012). Hexagonal Boron-Nitride (h-BN)

Report on growth of high quality h-BN High-quality h-BN single crystals were successfully grown around 1600℃ and 5 GPa

Strong cathodoluminescence signal at 215 nm = 5.765 eV (ultraviolet) More than 1000 times stronger than indirect free exciton luminescence h-BN has a direct bandgap

K. Watanabe et al., Nat. Mater. 3, 404 (2004). 谷口 尚 他, 高圧力の科学と技術 15, 4 (2005). Hexagonal Boron-Nitride (h-BN)

Nature Materials 2004

Nature Photonics 2016 Hexagonal Boron Nitride Black phosphorus Introduction to phosphorus Xene: graphene “like” 2D materials

Borophene Phospherene Arsenene Germanene Antimonene Stanene Bismuthene Black phosphorus vs graphene F. Xia et al., Nat. Rev. Phys. 1, 306 (2019). Graphene: hexagonal structure & flat

Black Phosphorus: two fold symmetry & puckered Stronger electronic coupling between layers More difficult to exfoliate Physical properties of black phosphorus

Black phosphorus: Semiconductor Band gap: 2 eV (monolayer = ) 0.2 eV (bulk)

Band gap (~0.2 eV) for 5-nm-thick device

L. Li et al., Nat. Nanotech 9, 372 (2014). Thickness-dependent properties

Transition metal dichalcogenides (TMDs) Difference between monolayer and bulk Bulk (crystal): Indirect band-gap semiconductor

Monolayer: Direct band-gap semiconductor Band gap is located at the K (K’) point. Similar to graphene with Dirac cones at K (K’) points

Slight difference of the lattice constant (bulk 3.135 A, monolayer 3.193 A)

H. Terrones et al., Sci. Rep. 3, 1549 (2013). Physical properties of black phosphorus Band structure as a function of # of layers

BP is always direct band-gap semiconductor A. Carvalho et al., Nat. Rev. Mat. 1, 1 (2016). Semiconducting TMDCs Physical properties of black phosphorus Electronic properties High on-off ratio (105 current modulation) 4 orders of magnitude larger than conventional Si-based transistor

Steeper increase of current

with Vg Current

L. Li et al., Nat. Nanotech 9, 372 (2014). Gate voltage Physical properties of black phosphorus “Bipolar” current Both carrier types are accessible

Hole carrier Mobility can reach up to 1000 cm2V-1s-1 Hall Hall coefficient

Electron carrier Gate voltage L. Li et al., Nat. Nanotech 9, 372 (2014). Physical properties of black phosphorus

Bandgap tuning by double gating

Device with 4 nm thick BP + top & Bottom gate

F. Xia et al., Nat. Rev. Phys. 1, 306 (2019). Physical properties of black phosphorus BP pn-junction 6-7 nm VP on the local gates Gate-defined pn junctions are possible

For global gating, strong modulation of Ids is observed

M. Buscema et al., Nat. Commun. 5, 4651 (2014). Physical properties of black phosphorus BP pn-junction Depending on the combination of electron or hole-doped gating between the two local gates, NP or PN junctions are possible Clear diode effect is observed for NP or PN junctions

M. Buscema et al., Nat. Commun. 5, 4651 (2014). Physical properties of black phosphorus Photocurrent/voltage under illumination M. Buscema et al., Nat. Commun. 5, 4651 (2014).

pn-junction generates finite photocurrent (ISC) with zero voltage bias

pn-junction generates finite photovoltage (VOC) with open circuit condition Physical properties of black phosphorus I-V characteristic under illumination: Increasing zero-bias I & open-circuit V Zero-bias I & open-circuit V (photocurrent & voltage) are observed at l in the near infrared range. M. Buscema et al., Nat. Commun. 5, 4651 (2014). Brief summary

Hexagonal Boron-Nitride (h-BN) is an insulator with a large gap (~6 eV) and good for encapsulating other 2D materials

Black Phosphorus (BP) is a direct gap semiconductor, independent of the thickness. The bandgap decreases with increasing thickness.

BP has a puckered structure and is not flat. It is also anisotropic in 2D.

BP has a gap and relatively high mobility (~103 cm2V-1s-1), therefore a good candidate for FET Xene Introduction to xene Xene: graphene “like” 2D materials

Borophene Phospherene Silicene Arsenene Germanene Antimonene Stanene Bismuthene Plumbene Introduction to xene p-bonding Xene is not flat due to a mixed sp2-sp3 character of bonding Free-standing xene is usually not flat

sp2

Larger lattice constant prevents p-bonding

sp3 Silicene Silicene: Si counterpart of graphene Slightly buckled structure is the most stable Semimetal & Dirac cone exists at K point

M. Houssa et al., J. Phys. Cond. Mat. 27, 253002 (2015). Silicene The most conventional substrate for the growth of Silicene: Ag(111) Similar lattice constant 4x4 buckled structure is formed Dirac cone like spectrum is observed by ARPES measurements

M. Houssa et al., J. Phys. Cond. Mat. 27, 253002 (2015). Silicene Silicene FET Silicene: Usually grown on a metallic substrate (e.g. Ag(111)) Transport measurements are difficult because of current shunting Silicene grown on Ag(111) and capped by Al2O3 can be delaminated by a blade

Ag layer can be used as electrodes after chemical etching with KI L. Tao et al., Nat. Nanotech. 10, 227 (2015). Silicene

Linear I-V character: Ohmic contact between silicene and Ag

Dirac peak like graphene is clearly observed L. Tao et al., Nat. Nanotech. 10, 227 (2015). Germanene Most stable state: Buckled honeycomb structure Regardless of the buckling, the Dirac cone exists at K points Similar to graphene Smaller p-bonding results in smaller splitting between bonding and antibonding states

A. Acun et al., J. Phys. Cond. Mat. 27, 443002 (2015). A. Acun et al., J. Phys. Cond. Mat. 27, 443002 (2015). Germanene

Bilayer graphene: AB stacking is naturally stable Bilayer germanene: AA stacking is naturally stable, similar bonding strength for inter- and intra-layer bonding Difficult to exfoliate

AB stacking AA stacking Germanene

Germanene can be grown by MBE on metallic substrates e.g. Pt(111), Au(111), Al(111) A. Acun et al., J. Phys. Cond. Mat. 27, 443002 (2015). Germanene on Pt(111) Germanene on Al(111) C. -C. Liu et al., Phys. Rev. Lett. 107, 076802 (2011). Topological properties of silicene and germanene Effective Hamiltonian for planar silicene

Same as graphene

Buckling enhances p-s coupling Increasing effective SOI Planar Silicene Low-buckled Silicene C. -C. Liu et al., Phys. Rev. Lett. 107, 076802 (2011). Topological properties of silicene and germanene

Topological gap engineering via buckling or strain More than one order of magnitude enhancement C. -C. Liu et al., Phys. Rev. Lett. 107, 076802 (2011). Topological properties of silicene and germanene Similar enhancement of the topological gap is possible Gap can be as large as 23.9 meV Nearly RT quantum spin Hall effect!

Planar Germanene Low-buckled Germanene Introduction to xene Xene: graphene “like” 2D materials

Borophene Phospherene Silicene Arsenene Germanene Antimonene Stanene Bismuthene Plumbene Spin-orbit interaction depends on atomic number The biggest advantage of graphene for spin transport

Atomic Number

Compared to silicene and germanene (based on Si and Ge), stanine (based on Sn) should be a better candidate as a 2D TI Topological properties of stanene Y. Xu et al., Phys. Rev. Lett. 111, 136804 (2013). Stanene: Topologically nontrivial (2D TI)

Topological gap can be enhanced by chemical functionalization

Functionalized stanenes (except by –H) exhibit enhanced topological gaps Topological properties of stanene Stanene: Band inversion occurs at K point

Fulorinated Stanene: The bands are gapped at K, and the band inversion occurs at G point

Stanane (with hydrogen): The bands are gapped at K and no band inversion at G Topologically nontrivial

Y. Xu et al., Phys. Rev. Lett. 111, 136804 (2013). Topological properties of stanene Band inversion occurs between bonding state of p-orbitals and anti-bonding state of s-orbital of Sn

Strongly depends on strain Y. Xu et al., Phys. Rev. Lett. 111, 136804 (2013). Epitaxial growth of stanene F. -f. Zhu et al., Nat. Mater. 14, 1020 (2015).

Bi2Te 3 (111) Similar lattice constant to that of stanene

Good candidate for the growth of stanene

STM images Modeled structure Epitaxial growth of stanene

Band structure of stanine on Bi2Te 3(111) F. -f. Zhu et al., Nat. Mater. 14, 1020 (2015).

Stanene on Bi2Te 3(111) Compressive strain Compressive strain makes stanine metallic No signatures of QSH state DFT results (Red: Stanene bands) Superconducting stanene Two states of bulk Sn: a-Sn & b-Sn a-Sn: Stable in thin limit, but semimetallic & non-superconductive b-Sn: Superconductive in bulk, but unstable in thin limit Stanene on PbTe: a-phase

M. Liao et al., Nat. Phys. 14, 344 (2018). Superconducting stanene

Tc of stanene strongly depends on the number of the layer

Tc of stanene also depends on the number of the layer of PbTe

M. Liao et al., Nat. Phys. 14, 344 (2018). Superconducting stanene

More surface vacancies for thicker PbTe

Superconductivity induced by electron-doping from PbTe substrates M. Liao et al., Nat. Phys. 14, 344 (2018). Electron pocket as # of PbTe layer increases Topological stanene Stanene: Usually buckled structure

Stanene on Cu(111): Ultraflat stanine, honeycomb lattice like graphene

J. Deng et al., Nat. Mater. 17, 1081 (2018). Topological stanene

A remarkable gap-opening at G (gap size ~ 300 meV)

Ultraflat stanene is owing to stretching, thereby it can gain adsorption energy onto Cu J. Deng et al., Nat. Mater. 17, 1081 (2018). ARPES measurements Topological stanene Scanning tunneling spectroscopy (STS) measurements (Conductance measurements) Enhanced conductance at the edge in the energy window between -1.2 eV and -1.45 eV Coincides with ARPES measurements, a signature of topological edge states

J. Deng et al., Nat. Mater. 17, 1081 (2018). Introduction to xene Xene: graphene “like” 2D materials

Borophene Phospherene Silicene Arsenene Germanene Antimonene Stanene Bismuthene Plumbene Borophene A. J. Mannix et al., Nat. Nanotech. 13, 444 (2018). Borophene: “The lightest metal”

Unique structures based on a triangular unit

Many metastable structures are theoretically predicted

Stable on Ag, Cu, Ni Stable on Ag(111) Borophene A. J. Mannix et al., Nat. Nanotech. 13, 444 (2018). Borophene: “The lightest metal”

Unique structures based on a triangular unit

Many metastable structures are theoretically predicted

Stable on Ag, Cu, Ni Stable on Ag(111) Borophene A. J. Mannix et al., Nat. Nanotech. 13, 444 (2018). Successful growth of borophene on Ag(111) 1D stripe phase (c & e) and rhombohedral (d & f) are observed Simulation Stripe phase=n1/6 phase STM

Rhombohedral phase=n1/5 phase Borophene Borophene on Ag(111) substrate Moiré pattern due to interface interaction b12 phase 3x1 onsite potential No modulation modulation Borophene

There are three equivalent domains in the Brillouin zone (BZ) due to the symmetry

Dirac cones are split around X (or M) points in the BZ Borophene Observation of split Dirac cones by ARPES Dirac cone and saddle point are observed from different cut images Clear signatures of Dirac fermions in borophene Plumbene Graphene’s “latest cousin” Buckled honeycomb lattice structure for “free- standing” plumbene

J. Yuhara et al., Adv. Mater. 1901017 (2019). Experimental report in March 2019 Plumbene Graphene’s “latest cousin” Buckled honeycomb lattice structure Quantum spin Hall state is predicted for the monolayer plumbene nanoribbon Plumbene Growth of plumbene on Pd(111) J. Yuhara et al., Adv. Mater. 1901017 (2019). Flat structure due to stretching by the substrate

Band structures are not observed yet Introduction to xene Xene: graphene “like” 2D materials

Borophene Phospherene Silicene Arsenene Germanene Antimonene Stanene Bismuthene Plumbene Antimonene Z. -Q. Shi et al., Adv. Mater. 31, 1806130 (2018). Antimonene: Monolayer of antimone (Sb)

Puckered honeycomb structure similar to BP, QSHE may be induced by strain

Monolayer growth by MBE on WTe2 Antimonene Scanning tunneling spectroscopy (STS) measurements: Finite differential conductance around the zero voltage Metallic nature

Z. -Q. Shi et al., Adv. Mater. 31, 1806130 (2018). Antimonene

Thicker antimonene is also possible

Metallic nature for thicker films: decreasing resistance when 10 or 20 layers of antimonene is demosited on WTe2

Z. -Q. Shi et al., Adv. Mater. 31, 1806130 (2018). Antimonene Stability in air

Except some adsorbates, multi-layer antimonene seems stable in air

Before exposure Exposure to O2 for 20 min Exposure to air for 12 h

Z. -Q. Shi et al., Adv. Mater. 31, 1806130 (2018). Antimonene M. Zhao et al., Sci. Rep. 5, 16108 (2015). QSHE by strain Antimonene Buckled structure as a free-standing form By tensile strain, antimonene can become 2D TI (possible on e.g. h-BN) Introduction of topological insulators Bilayer bismuth on (111) surface

[111]

Bilayer

Viewing from the top, it looks like a honeycomb lattice with a bucked structure. In [111] direction Bismuth crystal can be considered as a stack of such a bilayer structure. Ph. Hofmann, Prog. Sci. Surf. 81, 191 (2006). Bismuthene F. Reis et al., Science 357, 287 (2017). Bismuthene: Bi allotrope Unbuckled due to the large lattice constant of SiC(0001) Lattice is stretched due to the substrate to form a flat hexagonal lattice Bismuthene F. Reis et al., Science 357, 287 (2017). Without SOI: Dirac cone at K

Without intrinsic SOI, Dirac cone is gapped, and with intrinsic SOI+Rashba, band edges are spin-split ARPES Bismuthene px & py orbitals play a major role for the low energy states Strong onsite SOI drives the system into QSH state

Topological edge states are expected both for zigzag & armchair edges!

F. Reis et al., Science 357, 287 (2017). Bismuthene STM measurements at bismuthene/SiC(0001) steps Clear bulk band gap & edge conductance are observed Signatures of the QSHE F. Reis et al., Science 357, 287 (2017). Topological strainics for xene Strain from the substrate plays important roles for topological properties Compressive or tensile strain can switch the system between topologically trivial and non-trivial states (topological strainics) A. Molle et al., Nat. Mater. 16, 163 (2017). To be conitinued...

Arsenene

Monolayer Te Summary for Xene

Xene is a family 2D materials that do not exist naturally

For most of the xene mechanical exfoliation is difficult, and growth by molecular- beam epitaxy (MBE) on a substrate is needed

Due to the interaction with the substrate, xene is often more buckled or stretched than its free-standing form, which changes electronic properties

There are many xene which may become 2D topological insulators, and their topological nature is strongly modulated by strain

Since xene is often grown on a metallic substrate, transfer of xene to an insulating substrate is an issue to overcome