Generalized Gilat-Raubenheimer method for density-of-states calculation in photonic crystals

TL;DR

This paper introduces a generalized Gilat-Raubenheimer method for calculating the density of states in photonic crystals, applicable to all Bravais lattices, and demonstrates its superior accuracy over existing methods.

Contribution

A new affine transformation-based generalization of the Gilat-Raubenheimer method for DOS calculation in any Bravais lattice.

Findings

GGR method outperforms tetrahedron and Gaussian broadening methods

Successfully applied to gyroid photonic crystals with topological degeneracies

Provides accurate DOS calculations across various lattice types

Abstract

Efficient numeric algorithm is the key for accurate evaluation of density of states (DOS) in band theory. Gilat-Raubenheimer (GR) method proposed in 1966 is an efficient linear extrapolation method which was limited in specific lattices. Here, using an affine transformation, we provide a new generalization of the original GR method to any Bravais lattices and show that it is superior to the tetrahedron method and the adaptive Gaussian broadening method. Finally, we apply our generalized GR (GGR) method to compute DOS of various gyroid photonic crystals of topological degeneracies.