Atomic-Scale Visualization of Quasiparticle Interference on a Type-II Weyl Semimetal Surface

Hao Zheng, Guang Bian, Guoqing Chang, Hong Lu, Su-Yang Xu, Guangqiang Wang, Tay-Rong Chang, Songtian Zhang, Ilya Belopolski, Nasser Alidoust, Daniel S. Sanchez, Fengqi Song, Horng-Tay Jeng, Nan Yao, Arun Bansil, Shuang Jia, Hsin Lin, and M. Zahid Hasan

Phys. Rev. Lett. 117, 266804 – Published 23 December 2016

Abstract

We combine quasiparticle interference simulation (theory) and atomic resolution scanning tunneling spectromicroscopy (experiment) to visualize the interference patterns on a type-II Weyl semimetal ${Mo}_{x} W_{1 - x} {Te}_{2}$ for the first time. Our simulation based on first-principles band topology theoretically reveals the surface electron scattering behavior. We identify the topological Fermi arc states and reveal the scattering properties of the surface states in ${Mo}_{0.66} W_{0.34} {Te}_{2}$ . In addition, our result reveals an experimental signature of the topology via the interconnectivity of bulk and surface states, which is essential for understanding the unusual nature of this material.

Received 8 September 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.266804

Physics Subject Headings (PhySH)

Semimetals Weyl fermions

Weyl semimetal

Scanning tunneling microscopy Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hao Zheng¹, Guang Bian¹, Guoqing Chang^2,3, Hong Lu⁴, Su-Yang Xu¹, Guangqiang Wang⁴, Tay-Rong Chang⁵, Songtian Zhang¹, Ilya Belopolski¹, Nasser Alidoust¹, Daniel S. Sanchez¹, Fengqi Song⁶, Horng-Tay Jeng^5,7, Nan Yao⁸, Arun Bansil⁹, Shuang Jia^4,10, Hsin Lin^2,3, and M. Zahid Hasan^1,*

¹Laboratory for Topological Quantum Matter and Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore
³Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
⁴International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
⁵Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
⁶National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
⁷Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
⁸Princeton Institute for the Science and Technology of Materials, Princeton University, 70 Prospect Avenue, Princeton, New Jersey 08540, USA
⁹Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
¹⁰Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

^*mzhasan@princeton.edu

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Issue

Vol. 117, Iss. 26 — 23 December 2016

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Images

Figure 1
[(a) and (b)] Large-scale constant-current STM images ( $30 \times 18 {nm}^{2}$ ) of the ${Mo}_{0.66} W_{0.34} {Te}_{2} (001)$ surface taken at 100 and $- 100 mV$ , respectively. (c) and (d) are the enlarged images ( $5.3 \times 5.3 {nm}^{2}$ ) of the defect inside the square in (a) and (b), respectively. (e) and (f) are the atomically resolved experimental and simulated STM images ( $- 100 mV$ ), respectively. In both images, brighter color means higher charge density. Red dots mark the positions of surface Te atoms. The blue rectangles indicate surface unit cells. (g) The calculated density of state. (h) A typical $d I / d V$ spectrum on the ${Mo}_{0.66} W_{0.34} {Te}_{2}$ sample.
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Figure 2
[(a) and (b)] Schematics of the type-I and the type-II Weyl cone, respectively. (c) The calculated CEC in the first surface Brillouin zone (BZ) of ${Mo}_{0.66} W_{0.34} {Te}_{2} (001)$ at the energy of the Weyl node $W_{1}$ . The surface weight of states is indicated by color. Projected Weyl nodes are depicted by dots. The white and black colors stand for the opposite chiralities of the Weyl nodes. $e$ ( $h$ ) stands for the electron (hole) pocket. [(d) and (e)] The enlarged views of the area inside the yellow rectangle, drawn with a lower color contrast to enhance the visibility of the surface-state contours. The topological Fermi arc, which connects one pair of projected Weyl nodes, is clearly displayed and marked. Yellow and red dotted lines in (e) represent the boundaries of the projected hole and electron bulk pockets. (f) The $E − k$ dispersion cut along the white dashed line in (d). The Weyl node and Fermi arc are marked by white and yellow arrows, respectively.
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Figure 3
[(a)–(c)] The experimental QPI maps taken at the indicated voltages. The areas inside red rectangles contain only features from intra-BZ scatterings. Bragg points [( $2 π / a$ , 0) and (0, $2 π / b$ )] are marked on the images. [(d)–(f)] Theoretical QPI patterns derived from the surface-state-based calculations, which reasonably reproduce the features shown in the experimental data. In (b) and (e), white arrows point to the end points of the large crescent-shaped QPI contour while red arrows mark the small central features. [(g) and (h)] Experimental and theoretical $E − Q$ dispersions taken along the dashed line in (a). The white dotted lines in (h) are drawn to mark the edges of the simulated feature and are placed in (g) as a guide to the eye. The white (red) arrow here indicates the strongly (weakly) dispersed QPI signals as marked by the corresponding white (red) arrows in (b) and (e).
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Figure 4
(a) The calculated “complete” CEC that contains both bulk and surface state at $E = 50 meV$ . (b) The QPI pattern based on (a), which presents only the intra-BZ scattering. (c) The calculated CEC with only surface states considered. The Fermi arc is the central segment of the semicircular contours. (d) The QPI pattern based on (b). (e) The experimental QPI data (50 mV). The white dotted rectangles in (d) and (e) are located in the same position in $Q$ space and are the same size. (f) A cartoon demonstrating the sink effect of Weyl bulk states when the surface electron is scattered into a bulk pocket, a consequence of the topological bulk-surface connection. $e$ ( $h$ ) denotes the electron (hole) branch of a projected Weyl cone. Straight yellow lines represent the Fermi arcs. The solid arrow indicates the scattering between two surface Fermi arc states. The dotted arrow shows the process where an electron is scattered into one branch of a Weyl cone, and sinks into the bulk.
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