Discovery of a Three-Dimensional Topological Dirac Semimetal, Na
            <sub>3</sub>
            Bi

Liu, Zhongkai; Zhou, Bo; Zhang, Yi; Wang, Zhijun; Weng, Hongming; Prabhakaran, D.; Mo, S.-K.; Shen, Zhi‐Xun; Fang, Zhong; Dai, Xi; Hussain, Zahid; Chen, Yulin

doi:10.1126/science.1245085

Cited by 2,161 publications

(1,603 citation statements)

References 39 publications

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“…Another route which can result in the experimental verification of the novel WSM phase is to first realize a 3D Dirac semimetal and then break time reversal symmetry by applying a magnetic field, which will split a Dirac cone into a pair of Weyl nodes. Na 3 Bi and Cd 3 As 2 were recently proposed to be Dirac semimetals 27,28 , and also have been confirmed experimentally by a series of experiments [29][30][31][32][33][34][35][36][37] . In Bi 1−x Sb x for x ∼ 3 − 4% also the Dirac semimetal phase has been predicted [38][39][40] , and experimental signatures of realizing a WSM phase by breaking TR have been reported 41 .…”

Section: Introductionmentioning

confidence: 79%

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

Sharma¹,

Goswami²,

Tewari³

2016

Phys. Rev. B

183

191

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Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a non-trivial Berry curvature. Using semiclassical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TR-broken WSM also has an anomalous Nernst response due to a non-vanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (∇T ⊥ B) and the longitudinal (∇T B) set-up and confirm from our lattice model that in the parallel set-up, the Wiedemann-Franz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.

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Section: Introductionmentioning

confidence: 79%

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

Sharma¹,

Goswami²,

Tewari³

2016

Phys. Rev. B

183

191

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“…Such a material is known as 3D Dirac semimetal (DSM). [17][18][19][20][21][22][23][24][25][26] Around these points, the low-energy physics is described by a 4 × 4 massless Dirac Hamiltonian. In The Weyl Hamiltonian is quite robust against any perturbation.…”

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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“…Several materials have been theoretically predicted to be 3D DSMs 12,[17][18][19][20][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][36][37][38] the 3D DSM will evolve into WSM. Very recently, the predictions about WSM state in TaAs family 37,38 have been confirmed experimentally.…”

Section: Introductionmentioning

confidence: 99%

CaTe: a new topological node-line and Dirac semimetal

Du¹,

Tang²,

Wang³

et al. 2017

npj Quant Mater

115

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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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Discovery of a Three-Dimensional Topological Dirac Semimetal, Na ₃ Bi

Cited by 2,161 publications

References 39 publications

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

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

CaTe: a new topological node-line and Dirac semimetal

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Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi

Cited by 2,161 publications

References 39 publications

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

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

CaTe: a new topological node-line and Dirac semimetal

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Discovery of a Three-Dimensional Topological Dirac Semimetal, Na ₃ Bi