# Gapless surface states originated from accidentally degenerate quadratic band touching in a three-dimensional tetragonal photonic crystal

## TL;DR

This paper investigates gapless surface states in a tetragonal photonic crystal caused by accidental degeneracy at a high-symmetry point, demonstrating their formation and properties through theoretical and numerical analysis.

## Contribution

It introduces a new understanding of gapless surface states arising from accidental degeneracy in photonic crystals, supported by an effective Hamiltonian model and numerical validation.

## Key findings

- Gapless surface states occur at accidental degeneracy points.
- Effective Hamiltonian accurately describes the surface states.
- Numerical results agree with theoretical predictions.

## Abstract

A tetragonal photonic crystal composed of high-index pillars can exhibit a frequency-isolated accidental degeneracy at a high-symmetry point in the first Brillouin zone. A photonic band gap can be formed there by introducing a geometrical anisotropy in the pillars. In this gap, gapless surface/domain-wall states emerge under a certain condition. We analyze their physical property in terms of an effective hamiltonian, and a good agreement between the effective theory and numerical calculation is obtained.