Surface states of massive Dirac fermions with separated Weyl nodes

TL;DR

This paper analyzes the surface states of massive Dirac Hamiltonians with separated Weyl nodes, revealing how energy and momentum separation affect their dispersion and existence, relevant for understanding Weyl semimetals.

Contribution

It provides a detailed derivation of surface state spectra for massive Dirac Hamiltonians with separated Weyl nodes, highlighting the effects of energy and momentum separation.

Findings

Energy separation decreases Fermi velocity of surface states.

Surface states exist only within a finite momentum space strip.

Spectrum interpolates between Fermi arc and Dirac cone types.

Abstract

We derive the spectra of surface states for massive Dirac Hamiltonians with either momentum or energy separation between the left- and right-handed Weyl nodes. Momentum separation between the Weyl nodes corresponds to the explicitly broken time-reversal symmetry and the energy separation - to broken parity. Such Hamiltonians provide the simplest model description of Weyl semimetals. We find that the only effect of the energy separation between the Weyl nodes is to decrease the Fermi velocity in the linear dispersion relation of the surface states of massive Dirac Hamiltonian. In the case of broken time-reversal symmetry, the spectrum of surface states interpolates in a nontrivial way between the Fermi arc-type and the Dirac cone-type dispersion relations. In particular we find that for all values of the mass and the momentum separation between the Weyl nodes the surface states only exist in a strip of finite width in momentum space. We give also some simpler examples of surface states in order to make these notes more pedagogical.