Quantum description of Fermi arcs in Weyl semimetals in a magnetic field

TL;DR

This paper provides a quantum-mechanical analysis of Fermi arcs in Weyl semimetals under magnetic fields, replacing semiclassical models with detailed eigenstate calculations that match predictions.

Contribution

It introduces a quantum eigenstate framework for Fermi arcs in Weyl semimetals in magnetic fields, advancing beyond semiclassical descriptions.

Findings

Quantum eigenstates correspond to chiral Landau levels near Weyl nodes.

Surface states are coupled by evanescent contributions from all Landau levels.

Quantum results agree quantitatively with semiclassical predictions.

Abstract

For a Weyl semimetal (WSM) in a magnetic field, a semiclassical description of the Fermi-arc surface state dynamics is usually employed for explaining various unconventional magnetotransport phenomena, e.g., Weyl orbits, the three-dimensional Quantum Hall Effect, and the high transmission through twisted WSM interfaces. For a half-space geometry, we determine the low-energy quantum eigenstates for a four-band model of a WSM in a magnetic field perpendicular to the surface. The eigenstates correspond to in- and out-going chiral Landau level (LL) states, propagating (anti-)parallel to the field direction near different Weyl nodes, which are coupled by evanescent surface-state contributions generated by all other LLs. These replace the Fermi arc in a magnetic field. Computing the phase shift accumulated between in- and out-going chiral LL states, we compare our quantum-mechanical results to semiclassical predictions. We find quantitative agreement between both approaches.