Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

Abstract

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a spacedependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field B 5 is observable through an enhancement of the conductivity as σ ∼ B 2 5 due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B 5 on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of B 5 , revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as n ¼ 0 pseudo-Landau levels resulting from a B 5 confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B 5 creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to B 5 that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Strain-Induced Landau Levels in Arbitrary Dimensions with an Exact Spectrum

“…However, the resulting spectral quantization is approximate and restricted to energies near the Dirac point. Non-uniform strain has also been discussed for Weyl semimetals, but controlled effects are again restricted to the low-energy part of the spectrum [9][10][11].…”

Chiral magnetic plasmons in anomalous relativistic matter

“…Indeed, in Weyl materials, b 0 and b correspond to energy and momentum-space separations between the Weyl nodes, respectively. Strain-induced axial (or, equivalently, pseudoelectromagnetic) fields are described byà 5 ν , which is directly related to the deformation tensor [26][27][28][29][30]33]. As is easy to check, the consistent electric current, i.e.,…”

“…The last condition ensures the finiteness of integral at ω → ω + i0, which describes a gradual turning on of the oscillating fields. It is worth noting that forẼ = 0 the kinetic equation (29) reduces to the homogeneous equation considered in Ref. [43], where the effects of dynamical electromagnetism were not taken into account.…”

“…For example, as shown in Refs. [25][26][27][28][29][30], static mechanical strains applied to Weyl semimetals generate pseudomagnetic fields. As in graphene, the corresponding effective gauge fields capture the corrections to the kinetic energy of quasiparticles caused by unequal modifications of hopping parameters in a strained crystal.…”

“…[29,30] in the framework of chiral kinetic theory. This rather striking feature was interpreted as a pumping of the electric charge between the bulk and the boundary of the system.…”