Classification of stable three-dimensional Dirac semimetals with nontrivial topology

Abstract

A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant.

Large optical conductivity of Dirac semimetal Fermi arc surface states

“…(1) possesses only diagonal s 0 , s 3 terms, H 0 is block diagonal in spin space; the pair of 2×2 blocks (denoted s = ±1) are related via time-reversal symmetry (TRS) [1,2,4]. In contrast, H ∼ s 1 , s 2 is purely off-diagonal, coupling the s = ±1 blocks.…”

“…In contrast, H ∼ s 1 , s 2 is purely off-diagonal, coupling the s = ±1 blocks. Further, it is weak with H ∼ O(k 3 ), and vanishes along the k z axis due to rotational symmetry (RS) [1][2][3]. As a result, a pair of degenerate Dirac nodes emerge at ±q 0 where scattering between s = +1 and s = −1 blocks vanish.…”

“…Here, mass takes the form m q = −m 0 +m 1 k 2 z along the k z axis, with m 0 > 0 capturing band inversion [1,2] between the Dirac points ±k 0 = ± m 0 /m 1 .…”

“…Effective hamiltonian and surface states-We begin by considering three-dimensional topological Dirac semimetals (DSMs) [1,2,12] which possess rotational symmetry along the k z axis, and a pair of Dirac points at arXiv:1705.01566v1 [cond-mat.mes-hall] 3 May 2017 ±q 0 = (0, 0, ±k 0 ) within the Brillouin zone [3][4][5][6][7][8][9][10][11]. These can be described by a minimal 4×4 Hamiltonian [1,2,12],…”

“…Three-dimensional topological Dirac semimetals (DSMs) possess four-fold degenerate band touchings in the bulk (Dirac points) that are stabilized by the underlying crystal symmetries [1][2][3]. Of special interest are the unusual surface states in DSMs, which are localized on particular exposed crystal surfaces even in the presence of bulk metallic states.…”