Greens function of semi-infinite Weyl semimetals

TL;DR

This paper classifies boundary conditions in Weyl semimetals, showing how they influence Fermi arcs and Landau levels, with implications for understanding surface states and magnetic responses.

Contribution

It introduces a comprehensive classification of boundary conditions for Weyl semimetals and links them to observable surface phenomena and magnetic field effects.

Findings

Boundary conditions are classified into two types based on spin and chirality mixing.

Fermi arcs are accurately reproduced using the Greens function approach.

Only one class of boundary conditions leads to non-trivial Landau orbitals under magnetic fields.

Abstract

We classify all possible boundary conditions (BCs) for a Weyl material into two classes: (i) BC that mixes the spin projection but does not change the chirality attribute, and (ii) BC that mixes the chiralities. All BCs are parameterized with angular variables that can be regarded as mixing angles between spins or chiralities. Using the Greens function method, we show that these two BCs faithfully reproduce the Fermi arcs. The parameters are ultimately fixed by the orientation of Fermi arcs. We build on our classification and show that in the presence of a background magnetic field, only the second type BC gives rise to non-trivial Landau orbitals.