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 space-dependent 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 B5 is observable through an enhancement of the conductivity as σ∼B52 due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B5 on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of B5 , revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as n=0 pseudo-Landau levels resulting from a B5 confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B5 creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to B5 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.

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Plain Language Summary

Elastic deformations and inhomogeneities strongly affect a material’s electronic properties, for example, its conductance. Harnessing such deformations and inhomogeneities can potentially result in new material applications and technological advances. Here, we find that spatially varying strain and inhomogeneous magnetization enhance conductance in systems with a unique electronic structure: topological semimetals.

Topological semimetals, like Weyl and Dirac semimetals, exhibit quantum phenomena and are characterized by surface states (known as Fermi arcs). These, as well as other interface states associated with semimetallic topological phases, are consequences of a broader unifying concept: pseudo-Landau levels. Landau levels are quantum states of electrons in strong magnetic fields. Remarkably, inhomogeneities in topological semimetals act to generate effective magnetic fields for electrons, creating pseudo-Landau levels. Combining this observation with field theoretical, numerical, and semiclassical calculations, we provide theoretical evidence to support our findings of how the emergence of such pseudomagnetic fields can affect the main electronic properties of Weyl and Dirac semimetals. Our work, which builds on studies of strained graphene, presents two main advances that can drive immediate and long-term progress. In a practical sense, inhomogeneities in topological semimetals enhance the conductance, a quantity of primordial interest for applications. Conceptually, we show that pseudo-Landau levels, Fermi arcs, and magnetization bound currents are all aspects of the same phenomena. We expect that our results will soon be experimentally reproduced in solid-state setups as well as cold atomic systems.

Our findings establish strain engineering as a pathway to novel physics in semimetals and advance our understanding of the electronic states in these remarkable phases of matter.