Dirac semimetal and topological phase transitions inA3Bi (A=Na, K, Rb)

Abstract

The three-dimensional (3D) Dirac point, where two Weyl points overlap in momentum space, is usually unstable and hard to realize. Here we show, based on the first-principles calculations and effective model analysis, that crystalline A 3 Bi (A=Na, K, Rb) are Dirac semimetals with bulk 3D Dirac points protected by crystal symmetry. They possess non-trivial Fermi arcs on the surfaces, and can be driven into various topologically distinct phases by explicit breaking of symmetries. Giant diamagnetism, linear quantum magnetoresistance, and quantum spin-Hall effect will be expected for such compounds. PACS numbers: 71.20.-b, 73.20.-r, 73.43.-t 1 arXiv:1202.5636v2 [cond-mat.mtrl-sci]

CaTe: a new topological node-line and Dirac semimetal

“…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][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.…”

“…[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).…”

Topological semimetals with helicoid surface states

“…The surface states near the projection of a Dirac point is hence a superposition of a helicoid and an antihelicoid Riemann surface as shown in Fig.1(c), which cross each other along certain lines, and may have two Fermi arcs [15,16,45]. Yet, if there be no additional symmetry that protects their crossing, hybridization along the crossing lines opens a gap and the double-helicoid structure of the surface dispersion is lost and the Fermi arcs also disappear.…”

“…Double-helicoid Riemann surface state protected by one glide reflection symmetry in a Dirac semimetal A Dirac point can be considered as the superposition of two Weyl points with opposite Chern numbers [14,15], the same way the 3D massless Dirac equations decouple into two sets of Weyl equations [52]. The surface states near the projection of a Dirac point is hence a superposition of a helicoid and an antihelicoid Riemann surface as shown in Fig.1(c), which cross each other along certain lines, and may have two Fermi arcs [15,16,45].…”

“…The nontrivial topology gives rise to anomalous bulk properties of topological semimetals such as the chiral anomaly [3][4][5]. Several classes of topological semimetals have been theoretically proposed so far, including Weyl, [2,[6][7][8][9][10][11][12][13], Dirac [14][15][16][17] and nodal line semimetals [7,[17][18][19][20][21][22][23][24][25][26][27][28][29][30], some among which have been experimentally observed [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].Surface states of topological semimetals have attracted much attention. On the surface of a Weyl semimetal, the Fermi surface consists of open ar...…”