Spontaneous Chiral Ordering in Titanium Diselenide by Andre~s M. Mier Valdivia Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2018 ® Massachusetts Institute of Technology 2018. All rights reserved. A Signature redacted A u th or ...................... ........... Department of Physics May 11, 2018 Signature redacted C ertified by ...................... ..... Pablo D. Jarillo-Herrero Associate Professor of Physics Thesis Supervisor Signature redacted A ccepted by ................. ....... Scott A. Hughes Interim Associate Department Head, Department of Physics MAS CHUSS NO TE OF TEHNOLGY SEP 12 2018 LIBRARIES ARCHJVE9 2 Spontaneous Chiral Ordering in Titanium Diselenide by Andres M. Mier Valdivia Submitted to the Department of Physics on May 11, 2018, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract In this work, we studied the chiral charge density wave (CDW) phase in titanium diselenide (TiSe 2) with the circular photogalvanic effect (CPGE). Mechanically exfo- liated bulk TiSe 2 flakes were obtained and implemented into nanoscale devices using standard fabrication techniques. Four samples' photocurrent response to a 120 meV laser was subsequently measured as a function of temperature and laser power. The onset of the CPGE at approximately 174 K confirms the emergence of chiral order below the regular CDW transition at 197 K. Furthermore, we were able to train the chirality of the system by cooling it while shining circularly polarized light. With this study, we have confirmed that TiSe2 is a novel kind of material that spontaneously breaks inversion, all mirror, and roto-inversion symmetries and attains gyrotropic order, paving the way for future experimental work on similar condensed matter sys- tems. Thesis Supervisor: Pablo D. Jarillo-Herrero Title: Associate Professor of Physics 3 4 Acknowledgments I would like to thank Professor Pablo D. Jarillo-Herrero for the great opportunity to dive into the world of 2D materials. Thanks to his guidance, I have discovered my passion for the field and learned more than I could have ever expected. Furthermore, I would also like to thank Drs. Qiong Ma and Su-Yang Xu for their day-to-day help and patience. This work would not have been possible without them. I would also like to thank Yafang Yang for teaching me the foundations of nanofabrication during my initial time in the group. Furthermore, I am grateful to all members of the Jarillo- Herrero group for how welcoming and helpful they have been since I joined. Lastly, I would like to thank Wendi and my family for their constant support during my time at MIT. 5 6 Contents 1 Introduction 17 2 Overview of TMDs 19 2.1 Crystal Structure ......... ............ ....... 19 2.2 Electronic Structure ....... ............ ....... 19 2.3 O ptical Properties ........... ................ 21 3 Charge Density Wave Physics 23 3.1 The Peierls Transition ........... ........... ... 23 3.2 Electrical Properties of CDWs ....... ........... ... 25 4 The Charge Density Wave in 1T-TiSe 2 27 4.1 The CDW Transition ............... .............. 28 4.2 Experimental Evidence for a Chiral CDW .............. 31 4.3 A Model for a Chiral CDW .... ... ...... ........ 35 4.4 The CPGE as a Probe for Chirality .... ... .... .... ... 37 4.5 Degradation .................... ..... ...... ... 37 5 The Circular Photogalvanic Effect 41 5.1 Phenom enology ........ ........... .......... 41 5.2 CPGE in Weyl Semimetals .. ........... .......... 42 5.3 The CPGE and Chiral Charge Ordering . ........... ... 43 6 Device Fabrication 45 7 6.1 Bottom Contacts ......... .................... 45 6.1.1 Electron Beam Lithography ................... 45 6.1.2 Metal Deposition .. ....................... 45 6.2 Exfoliation ........ ......................... 46 6.2.1 TiSe 2 .......... ............. ......... 46 6.2.2 Graphene and hBN .............. .......... 49 6.3 Transfer .................................. 50 6.3.1 PC Slide Fabrication ..... .................. 50 6.3.2 Transfer Set Up ........ .................. 51 6.3.3 Pick up .............................. 51 6.3.4 Transfer ... ....................... .... 54 6.3.5 TiSe2, Graphene and hBN .................... 54 6.4 Devices ......... ......................... 55 6.4.1 Devices 1 and 2 .......................... 55 6.4.2 Devices 3 and 4 .......................... 56 7 Results and Analysis 57 7.1 Measurement Set Up ........................... 57 7.2 Large Linear Photogalvanic Effect .......... .......... 57 7.3 Chiral Training ......................... ..... 59 7.4 Chiral Transition ............................. 62 7.5 Discussion ....................... .......... 64 8 Conclusion 67 8 List of Figures 2-1 (a) TMDs consist of transition metal M atoms sandwiched between chalcogen X atoms. (b) The most common crystallographic phases observed in TMDs. Figures adapted from [1] [2]. .. ........ .. 20 2-2 A table summarizing TMD crystal structure and observed electronic phases based on the transition metal. Figure adapted from [1]. ... 20 3-1 The Peierls transition in a ID metal. (a) A ID atomic lattice with constant a. p(r) is the electron density; in this case it is constant. The Brillouin zone is shown below it, and only the energy levels up the Fermi level EF are filled (EF in the figure). (b) Because the metal is unstable at T = 0 K, a gap opens at the Fermi level and a superlattice with spacing 2a forms. The Brillouin zone reduces to half of its original size and leads to band folding at kF. Figures adapted from [31. .. 24 3-2 Typical current versus electric field behavior for CDW conductors. There is no conductance below ET, after which charge order slides rel- ative to the lattice and generates a current. In this particular graph, the data is for NbSe3 at 120 K. Figure adapted from [4]. ...... 25 3-3 When ET is overcome, the CDW slides. The lattice atoms oscillate, as traced by the yellow path that follows the position of the red particle. The effect allows the potential to move towards the right, illustrated by the traveling black arrow. Figure adapted from [4]. ... ..... 26 9 4-1 Crystal structure of 1T-TiSe 2. The purple atoms are Ti, and the green are Se. (a) Top view of a monolayer. (b) Crystal sideview. (c) B rillouin zone. ..... ...... ...... ...... ...... .. 27 4-2 ARPES data for monolayer TiSe2. (a) In solid black: the normal-state Brillouin zone of TiSe 2. In dashed red: the reduced Brillouin zone in the CDW phase. (b) On the left: the normal state ARPES data taken at room temperature. On the right: the CDW state ARPES data taken at 10 K. Note the appearance of a new band at M/IF due to band folding. Figures adapted from [5]. ..... ........ .... 28 4-3 Temperature dependence of the band gap as measured from the ARPES spectra for monolayer TiSe 2. The solid blue line is a BCS-type fit. The dashed red line is a linear approximation. The BCS-type fit gives TCDW = 232 5 K. Figure adapted from [5]. .. .... ..... ... 29 4-4 Thickness dependence of TCDW for TiSe2. The individual plots show the band gap evolution from ARPES data versus temperature. The transition temperatures were computed with a BCS-type fit. (a) Mono- layer data with TCDW = 232 t 5 K. (b) Bilayer data. Note that there are two transition temperatures at TcDw,1 = 236 5 K and TCDW,2 = 195 3 K. (c) Trilayer data with TCDW = 203 3 K. (d) 6-layer data with TCDW = 205 3 K. Figure adapted from [6]. .... 30 4-5 STM data for a bulk TiSe2 sample at 84 K. (a) Real space STM data where the CDW is apparent. The ai vectors designate the three crystallographic directions, and the qi indicate the directions of charge modulation. (b) Line intensities along the three distinct qi in real space. (c) Fourier transform of (a). Note how the intensity increases CCW from q3 to qi. (d) Line intensities along the different qi in Fourier space. Figure adapted from [7]. ... ...... ...... .. 31 10 4-6 (a) A real space 12 nm x 12 nm STM image of a sample at 6.3 K. The blue lines denote the domain wall between the CW and CCW chiral phases. (b) and (c): the Fourier transform of the data enclosed by the squares in the CW and CCW regions, respectively. Figure adapted from [7]. ........ .......... .......... ...... 32 4-7 Data take n at 4.6 K. (a) A 20 nm x 10 nm STM image of a step between two successive TiSe2 layers. The inset shows the height dif- ference between the layers of 6 A, corresponding to the size of one Se-Ti-Se sandwich. (b), (c) An enlargement of the white squares in (a) corresponding to defects in the bottom and top layers, respectively. The circles highlight the charge maxima, and the arrows indicate the direction of atomic displacements. (d), (e) 2.8 nm x 2.8 nm STM images of the bottom and top layers, respectively, showing that the orientation of the qj is the same for both.(f), (g) Fast FT of (d), (e) where the blue circles highlight extra features owing to the CDW. Figure adapted from [8] ... ...... ..... ...... ..... 33 4-8 Evidence for a phase transition at 183 K. (a) X-ray diffraction peak intensities as a function of temperature. The red points follow a peak sensitive to the formation of the regular CDW superlattice. The blue data is for another peak that turns on around 183 K. (b) Specific heat as a function of temperature. (c) Resistivity anisotropy as a function of temperature. Figures adapted from [9]. ...... ..... .... 34 4-9 Illustration of the Brillouin zone and the three inequivalent directions for orbital and charge ordering. Figure adapted from [101 . ...... 35 4-10 Room temperature resistivity as a function of time (in days) for an 11 nm TiSe2 thick flake. The resistivity shows a clear increase around 12 days, and a large spike after 15 days. Figure adapted from [11]. .. 38 11 4-11 Degradation in TiSe2. (a),(b) TEM images of TiSe2 mounted on Si3 N 4 shortly after exfoliation and after a month of exposure to air, respec- tively.