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Title: Discovery of Lorentz-violating type II Weyl fermions in LaAlGe

Abstract

In quantum field theory, Weyl fermions are relativistic particles that travel at the speed of light and strictly obey the celebrated Lorentz symmetry. Their low-energy condensed matter analogs are Weyl semimetals, which are conductors whose electronic excitations mimic the Weyl fermion equation of motion. Although the traditional (type I) emergent Weyl fermions observed in TaAs still approximately respect Lorentz symmetry, recently, the so-called type II Weyl semimetal has been proposed, where the emergent Weyl quasiparticles break the Lorentz symmetry so strongly that they cannot be smoothly connected to Lorentz symmetric Weyl particles. Despite some evidence of nontrivial surface states, the direct observation of the type II bulk Weyl fermions remains elusive. We present the direct observation of the type II Weyl fermions in crystalline solid lanthanum aluminum germanide (LaAlGe) based on our photoemission data alone, without reliance on band structure calculations. Furthermore, our systematic data agree with the theoretical calculations, providing further support on our experimental results.

Authors:
 [1];  [2]; ORCiD logo [3];  [4]; ORCiD logo [3];  [1];  [1];  [4];  [5];  [1]; ORCiD logo [6];  [4]; ORCiD logo [7]; ORCiD logo [3]; ORCiD logo [8];  [9];  [10];  [11];  [12]; ORCiD logo [3] more »;  [13];  [1] « less
  1. Princeton Univ., Princeton, NJ (United States)
  2. Princeton Univ., Princeton, NJ (United States); Rigetti & Co Inc., Berkeley, CA (United States)
  3. National Univ. of Singapore (Singapore)
  4. Peking Univ., Beijing (China)
  5. Princeton Univ., Princeton, NJ (United States); Univ. of Missouri, Columbia, MO (United States)
  6. Paul Scherrer Inst. (PSI), Villigen (Switzerland); National Institute of Materials Physics, Magurele (Romania)
  7. National Univ. of Singapore (Singapore); National Sun Yat-Sen Univ., Kaohsiung (Taiwan)
  8. National Tsing Hua Univ., Hsinchu (Taiwan); National Cheng Kung Univ., Tainan (Taiwan)
  9. National Tsing Hua Univ., Hsinchu (Taiwan); Academia Sinica, Taipei (Taiwan)
  10. Northeastern Univ., Boston, MA (United States)
  11. Univ. of Zurich, Winterthurerstrasse (Switzerland)
  12. Paul Scherrer Inst. (PSI), Villigen (Switzerland)
  13. Peking Univ., Beijing (China); Collaborative Innovation Center of Quantum Matter, Beijing (China)
Publication Date:
Research Org.:
Northeastern Univ., Boston, MA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1473922
Grant/Contract Number:  
FG02-07ER46352; FG02-05ER46200; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Science Advances
Additional Journal Information:
Journal Volume: 3; Journal Issue: 6; Journal ID: ISSN 2375-2548
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Topological Materials; Weyl semimetals

Citation Formats

Xu, Su -Yang, Alidoust, Nasser, Chang, Guoqing, Lu, Hong, Singh, Bahadur, Belopolski, Ilya, Sanchez, Daniel S., Zhang, Xiao, Bian, Guang, Zheng, Hao, Husanu, Marious -Adrian, Bian, Yi, Huang, Shin -Ming, Hsu, Chuang -Han, Chang, Tay -Rong, Jeng, Horng -Tay, Bansil, Arun, Neupert, Titus, Strocov, Vladimir N., Lin, Hsin, Jia, Shuang, and Hasan, M. Zahid. Discovery of Lorentz-violating type II Weyl fermions in LaAlGe. United States: N. p., 2017. Web. doi:10.1126/sciadv.1603266.
Xu, Su -Yang, Alidoust, Nasser, Chang, Guoqing, Lu, Hong, Singh, Bahadur, Belopolski, Ilya, Sanchez, Daniel S., Zhang, Xiao, Bian, Guang, Zheng, Hao, Husanu, Marious -Adrian, Bian, Yi, Huang, Shin -Ming, Hsu, Chuang -Han, Chang, Tay -Rong, Jeng, Horng -Tay, Bansil, Arun, Neupert, Titus, Strocov, Vladimir N., Lin, Hsin, Jia, Shuang, & Hasan, M. Zahid. Discovery of Lorentz-violating type II Weyl fermions in LaAlGe. United States. https://doi.org/10.1126/sciadv.1603266
Xu, Su -Yang, Alidoust, Nasser, Chang, Guoqing, Lu, Hong, Singh, Bahadur, Belopolski, Ilya, Sanchez, Daniel S., Zhang, Xiao, Bian, Guang, Zheng, Hao, Husanu, Marious -Adrian, Bian, Yi, Huang, Shin -Ming, Hsu, Chuang -Han, Chang, Tay -Rong, Jeng, Horng -Tay, Bansil, Arun, Neupert, Titus, Strocov, Vladimir N., Lin, Hsin, Jia, Shuang, and Hasan, M. Zahid. Fri . "Discovery of Lorentz-violating type II Weyl fermions in LaAlGe". United States. https://doi.org/10.1126/sciadv.1603266. https://www.osti.gov/servlets/purl/1473922.
@article{osti_1473922,
title = {Discovery of Lorentz-violating type II Weyl fermions in LaAlGe},
author = {Xu, Su -Yang and Alidoust, Nasser and Chang, Guoqing and Lu, Hong and Singh, Bahadur and Belopolski, Ilya and Sanchez, Daniel S. and Zhang, Xiao and Bian, Guang and Zheng, Hao and Husanu, Marious -Adrian and Bian, Yi and Huang, Shin -Ming and Hsu, Chuang -Han and Chang, Tay -Rong and Jeng, Horng -Tay and Bansil, Arun and Neupert, Titus and Strocov, Vladimir N. and Lin, Hsin and Jia, Shuang and Hasan, M. Zahid},
abstractNote = {In quantum field theory, Weyl fermions are relativistic particles that travel at the speed of light and strictly obey the celebrated Lorentz symmetry. Their low-energy condensed matter analogs are Weyl semimetals, which are conductors whose electronic excitations mimic the Weyl fermion equation of motion. Although the traditional (type I) emergent Weyl fermions observed in TaAs still approximately respect Lorentz symmetry, recently, the so-called type II Weyl semimetal has been proposed, where the emergent Weyl quasiparticles break the Lorentz symmetry so strongly that they cannot be smoothly connected to Lorentz symmetric Weyl particles. Despite some evidence of nontrivial surface states, the direct observation of the type II bulk Weyl fermions remains elusive. We present the direct observation of the type II Weyl fermions in crystalline solid lanthanum aluminum germanide (LaAlGe) based on our photoemission data alone, without reliance on band structure calculations. Furthermore, our systematic data agree with the theoretical calculations, providing further support on our experimental results.},
doi = {10.1126/sciadv.1603266},
journal = {Science Advances},
number = 6,
volume = 3,
place = {United States},
year = {Fri Jun 02 00:00:00 EDT 2017},
month = {Fri Jun 02 00:00:00 EDT 2017}
}

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Figures / Tables:

Fig. 1 Fig. 1: Topology and BZ symmetry of LaAlGe. (A) Body-centered tetragonal structure of LaAlGe, with space group I41md (109). The structure consists of stacks of La, Al, and Ge layers, and along the (001) direction, each layer consists of only one type of element. (B) The bulk and (001) surfacemore » BZ. (C) First-principles band structure calculations along high-symmetry directions without spin-orbit coupling (SOC). (D) Momentum space configuration of the four nodal lines (two on the kx = 0 and two on the ky = 0 mirror planes) denoted by the rings, as well as the four spinless pairs of Weyl nodes denoted as W3 on the kz = 0 plane, in the absence of SOC. Blue and red colors indicate positive and negative chiralities, respectively. (E) Configuration of the 40 Weyl nodes in the bulk BZ created upon the inclusion of SOC. The nodal lines are gapped out by SOC, and 24 Weyl nodes emerge in the vicinity of the nodal lines. In addition, each spinless W3 Weyl node splits into two spinful Weyl nodes of the same chirality, which we denote as W3′ and W3″. Hence, the eight W3 without SOC evolve into eight W3′ and eight W3′′ Weyl nodes with SOC. Therefore, in total, there are 40 Weyl nodes. For the 24 Weyl nodes that emerge from the gapping of the nodal line, we denote the 8 Weyl nodes that are near the boundaries of kz = 0 plane as W1 and the other 16 that are away from the $k$z = 0 plane as W2. The W3′ and W3′′ are also on the kz = 0 plane, but they are near the diagonal lines. (F) Projection of the Weyl nodes on the (001) surface BZ in one quadrant. (G) Schematics comparing the three types of Weyl nodes appearing upon the inclusion of SOC. The W2 nodes are type II Weyl nodes, whereas the W1, W3′, and W3′′ nodes are type I. W2 Weyl nodes are located almost exactly at the Fermi level, whereas W1, W3′, and W3′′ Weyl nodes are about 60, 110, and 130 meV above the Fermi level, respectively. (H) Core level measurement of the studied samples, which clearly shows the expected La, Al, and Ge peaks. a.u., arbitrary units.« less

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