Discovery of a Weyl fermion semimetal and topological Fermi arcs

Xu, Su-Yang; Belopolski, Ilya; Alidoust, Nasser; Neupane, Madhab; Zhang, Chenglong; Sankar, Raman; Huang, Shin-Ming; Lee, Chi-Cheng; Chang, Guoqing; Wang, Baokai; Bian, Guang; Zheng, Hao; Sanchez, Daniel S.; Chou, F. C.; Lin, Hsin; Jia, Shuang; Hasan, M. Zahid

doi:10.1126/science.aaa9297

Cited by 3,234 publications

(2,706 citation statements)

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“…Note that superselected states do not necessary have a fixed number of particles, and we believe that a coherent superposition (not a mixture) of states with different numbers of fermionic quasiparticles can be observed in future experiments [20][21][22]. From a mathematical viewpoint, it is interesting to find all possible states with equispectral mode-reduced states.…”

Section: Spectra Of Mode-reduced Statesmentioning

confidence: 99%

“…Thus, the experimental investigations of nature modify our understanding of fundamental symmetries, the physical models, and the mathematical frameworks used for their description. Recent experiments with massless Weyl fermionic quasiparticles [20][21][22] stimulate us to investigate properties of fermionic states in coherent superpositions of different number states. Moreover, superpositions of different number states usually emerge in fermionized models (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Spectral properties of reduced fermionic density operators and parity superselection rule

Amosov

Filippov

2016

Quantum Inf Process

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We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that spectra of mode-reduced states are not identical in general and fully characterize pure states with equispectral mode-reduced states. Such states are related via local unitary operations with states satisfying the parity superselection rule. Thus, valid purifications for fermionic density operators are found. To get particle-reduced operators for a general system, we introduce the operation Φ(̺) = i ai̺a † i . We conjecture that spectra of Φ p (̺) and conventional p-particle reduced density matrix ̺p coincide. Nontrivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

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Section: Spectra Of Mode-reduced Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectral properties of reduced fermionic density operators and parity superselection rule

Amosov

Filippov

2016

Quantum Inf Process

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“…Very recently, the predictions about WSM state in TaAs family 37,38 have been confirmed experimentally. [39][40][41][42] Unlike DSM and WSM whose band crossing points distribute at separate k points in the BZ, for a NLS the crossing points around the Fermi level form a closed loop. Several compounds have been proposed as NLSs, including Mackay-Terrones crystals, 25 Bernal graphite, 43 hyperhoneycomb lattices, 44 and antiperovskite Cu 3 PdN 26,27 and Cu 3 NZn.…”

Section: Introductionmentioning

confidence: 99%

CaTe: a new topological node-line and Dirac semimetal

Du¹,

Tang²,

Wang³

et al. 2017

npj Quant Mater

114

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Combining first-principles calculations and effective model analysis, we predict that CaTe is a topological node-line semimetal in the absence of the spin-orbit coupling. Using a slab model, we obtain the nearly flat drumhead surface state near the Fermi level. When the spin-orbit coupling is included, three node lines will evolve into a pair of Dirac points along the M−R line. These Dirac points are robust and protected by the C 4 rotation symmetry. Once this crystal symmetry is broken, the Dirac points will be eliminated, and the system becomes a strong topological insulator.npj Quantum Materials (2017) 2:3 ; doi:10.1038/s41535-016-0005-4 INTRODUCTIONTopological insulator (TI) has attracted broad interest in the past 10 years. [1][2][3][4][5][6][7] The unique property of TI is that it is an insulator in the bulk but has exotic metallic surface states due to the topological order. More recently, the research on topological states has been extended to three-dimensional (3D) semimetal systems. [8][9][10][11][12] These systems could demonstrate many fascinating phenomena, such as Weyl fermion quantum transport and various Hall effects, [13][14][15][16] consequently become the rising stars of the field. Up to now, three kinds of topological semimetals have been discovered, i.e., 3D Dirac semimetal (DSM), 12,[17][18][19][20][21] Weyl semimetal (WSM), 8,9,22,23 and node-line semimetal (NLS). [24][25][26][27][28][29] The 3D DSM has four-fold degeneracy point, which can be viewed as the kiss of two Weyl fermions with opposite chiralities in the Brillouin zone (BZ). Protected by the crystal symmetry and time reversal symmetry, 3D DSMs can be robust against external perturbations. Several materials have been theoretically predicted to be 3D DSMs 12,17-21 and some of them have already been confirmed by experiments. [30][31][32][33] If one breaks the time reversal symmetry 8,22,23,34 or the inversion symmetry, 35-38 the 3D DSM will evolve into WSM. Very recently, the predictions about WSM state in TaAs family 37,38 have been confirmed experimentally. [39][40][41][42] Unlike DSM and WSM whose band crossing points distribute at separate k points in the BZ, for a NLS the crossing points around the Fermi level form a closed loop. Several compounds have been proposed as NLSs, including Mackay-Terrones crystals, 25 Bernal graphite, 43 hyperhoneycomb lattices, 44 and antiperovskite Cu 3 PdN 26,27 and Cu 3 NZn. 27 In the absence of spin-orbit coupling (SOC), time reversal symmetry together with inversion or mirror symmetry will guarantee the occurrence of node line in 3D BZ for systems with band inversion. [25][26][27]37,45,46 Same with TI and WSM, NLS also has a characteristic surface state, namely, drumhead-like state. 24-29 Such a 2D flat band surface state may become a route to achieve high temperature superconductivity. 47,48 As a result, it is of great impetus to search new NLS.In this study, based on first-principles calculations and effective model analysis, we propose that CaTe in CsCl-type structure is a NLS with drumhea...

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“…4 Weyl semimetal (WSM) has linear despersion around two-fold degenerate band-crossing points, [5][6][7][8][9][10][11][12][13][14] and the Weyl point possesses a definite chirality of ±1, around which the quasiparticle excitation is anolog of Weyl fermions. 4,15 Furthermore, it could be viewed as the monopole of Berry flux in momentum space, and the two Weyl points with opposite chiralities correspond to the source and drain respectively.…”

Section: Introductionmentioning

confidence: 99%

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

Chen

Zhang

et al. 2017

J. Phys. Chem. C

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Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing points with linear dispersion, around which the quasiparticles resemble the relativistic Dirac Fermions. It can be described by a 4 × 4 massless Dirac Hamiltonian which can be decomposed into a pair of Weyl points or gaped into an insulator. Thus, crystal symmetry is critical to guarantee the stable existence. On the contrary, by breaking crystal symmetry, a DSM may transform into a Weyl semimetal (WSM) or a topological insulator (TI). Here, by taking hexagonal LiAuSe as an example, we find that it is a starfruit shaped multiple nodal chain semimetal in the absence of spin-orbit coupling 1 arXiv:1712.01475v1 [cond-mat.mtrl-sci] 5 Dec 2017 (SOC). In the presence of SOC, it is an ideal DSM naturally with the Dirac points locating at Fermi level exactly, and it would transform into WSM phase by introducing external Zeeman field or by magnetic doping with rare-earth atom Sm. It could also tranform into TI state by breaking rotational symmetry. Our studies show that DSM is a cirtical point for topological phase transition, and the conclusion can apply to most of the DSM materials, not limited to the hexagonal material LiAuSe.2

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Discovery of a Weyl fermion semimetal and topological Fermi arcs

Cited by 3,234 publications

References 32 publications

Spectral properties of reduced fermionic density operators and parity superselection rule

Spectral properties of reduced fermionic density operators and parity superselection rule

CaTe: a new topological node-line and Dirac semimetal

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

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