Anomalous Hall transport in tilted multi-Weyl semimetals

Abstract

We study the effect of a perpendicular magnetic field B on a multinode Weyl semimetal (mWSM) of arbitrary integer monopole charge n, with the two Weyl multinodes separated in k-space. Besides type-I mWSMs, there exist type-II mWSMs which are characterized by the tilted minimal dispersion for low-energy excitations; the Weyl points in type-II mWSMs are still protected crossings but appear at the contact of the electron and hole pockets, after the Lifshitz transition. We find that the presence of a perpendicular magnetic field quantizes the occupation pockets due to the presence of Fermi tubes. In this theory, the Hilbert space is spanned by a set of n chiral degenerate ground states, and a countably infinite number of particle-hole symmetric Landau levels (LLs). We calculate the Hall conductivity for the tilt-symmetric case of type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and recover the well-known vacuum contribution. We compute the Fermi surface corrections and show that the expression generalizes from the formula for elementary (n = 1) type-I WSMs. We derive an expression for the type-II mWSM Hall conductivity, which is bounded by a LL cutoff introduced on physical grounds. Interestingly, we find that the anomalous vacuum Hall conductivity is vanishing in the type-II phase at all temperatures. The corresponding thermal Hall and Nernst conductivities are evaluated and characterized for both phases. The qualitative and quantitative observations presented here may serve in the characterization of generic mWSMs of both types.

Non-Linear Hall Effect in Multi-Weyl Semimetals

“…We begin with a low energy model Hamiltonian 74,75 that describes the multi-Weyl semimetals effectively. Setting = 1, the Hamiltonian reads…”

Valley-dependent time evolution of coherent electron states in tilted anisotropic Dirac materials

“…Several two-dimensional materials such as 8 − pmmn borophene [4,5,33,39], strained graphene [17], Weyl semimetals [40,43,44], and the organic compound α-(BEDT-TTF) 2 I 3 [11,32,34,36] present a tilted Dirac cone in the low electronic band structure. The electronic properties of the tilted anisotropic Dirac materials are described by the continuous Dirac Hamiltonian…”

“…Meanwhile, the anisotropy induced by strainengineering in graphene has led to the possibility of obtaining pseudo-magnetic fields [15,16], the tuning of electronic and optical properties [17][18][19][20][21][22][23][24][25][26][27], valley polarized currents [28,29], and anomalous tunneling [30,31]. The electronic and transport properties are valley-dependent due to the tilting of Dirac cones, as shown in the relative spacing of Landau levels [11,32,33], pseudo-magnetic fields [4], and other physical properties [8,9,17,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. These singular features motivate the investigation of unusual effects by the intrinsic Dirac cone tilt.…”

Fermi arcs of topological surface states in multi-Weyl Semimetals

“…In fact, not only there are Dirac and Weyl points, but also there are other exotic Weyl points of higher chirality which could exist in condensed matter physics under the protection of crystalline symmetries, such as multi-Weyl topological semimetal with partial non-linear dispersion, spin-1 excitations with threefold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions [23][24][25][26] . In which the so called multi-Weyl semimetals are really amazing [27][28][29][30][31][32] . However, so far as the authors are informed, the Fermi arc of topological surface states in Multi-Weyl semimetal has not been investigated analytically in literature due to their nonlinear dispersion relation near Multi-Weyl points.…”