Symmetry-protected Interface Modes Bifurcated from Double Dirac Cones

TL;DR

This paper rigorously proves the existence and symmetry protection of interface modes bifurcating from double Dirac cones due to band inversion, using a discrete layer-potential framework.

Contribution

It provides a rigorous proof of interface modes bifurcating from double Dirac cones and establishes their symmetry protection under certain perturbations.

Findings

Existence of interface modes bifurcating from double Dirac cones.

Number of interface modes determined explicitly.

Interface modes are symmetry-protected against reflection-symmetry-respecting perturbations.

Abstract

We rigorously prove the existence of interface modes in a sharp interface model, which bifurcate from the double Dirac cone as a consequence of the band inversion induced by super-symmetry breaking. The exact number of interface modes are determined. The proof is based on a discrete version of the layer-potential framework. Moreover, we prove that such interface modes are symmetry-protected against perturbations that respect the reflection symmetry.