Generalization of Chiral Symmetry for Tilted Dirac Cones

TL;DR

This paper extends the concept of chiral symmetry to tilted Dirac cones, revealing that a non-hermitian generalized symmetry protects zero modes and relates to the ellipticity of the Dirac Hamiltonian.

Contribution

It introduces a generalized, non-hermitian chiral symmetry for tilted Dirac cones and links it to the protection of zero modes and the elliptic nature of the Hamiltonian.

Findings

Generalized chiral symmetry protects zero modes in tilted Dirac cones.

The symmetry is equivalent to the Dirac Hamiltonian being elliptic.

The work connects symmetry protection to index theorem concepts.

Abstract

The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects the zero modes (n=0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.