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 non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field $\mathbf{B}_{5}$ is observable through an enhancement of the conductivity as $\sigma\sim \mathbf{B}_{5} ^{2}$ due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of $\mathbf{B}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of $\mathbf{B}_5$, 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 $\mathbf{B}_5$ confined to the surface (ii) as a consequence of position-momentum locking a bulk $\mathbf{B}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to $\mathbf{B}_{5}$ 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.
Highlights
Electronic and lattice degrees of freedom are inevitably intertwined in solid-state physics [1]
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 1⁄4 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
II, we review how inhomogeneous strain in timereversal-invariant Weyl and Dirac semimetals leads to an effective axial magnetic field or, alternatively, a space-dependent Weyl node separation
Summary
Electronic and lattice degrees of freedom are inevitably intertwined in solid-state physics [1]. Such a concept, considered recently in some detail for real magnetic fields in Weyl semimetals [25,26], will be of use here We find that these results significantly depart from the naive expectation gained from studies of strained graphene [3,4,5] from which the bulk zeroth pseudo-Landau level is expected to have opposite chirality with respect to the Fermi arcs [13,27]. III, we predict the enhancement of the conductivity of Weyl and Dirac semimetals due to a uniform axial magnetic field and relate it to the underlying associated chiral pseudomagnetic effect The latter leads to bound currents flowing within the material and along the boundary, even in equilibrium, as well as an enhanced bulk longitudinal conductivity. V, we provide a discussion and proposals to experimentally observe the discussed phenomena
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
