Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation

TL;DR

This study compares four computational methods for modeling the optical response of crystals, revealing that length gauge approaches yield more accurate and convergent results, especially in truncated band models.

Contribution

It systematically analyzes the effects of basis truncation on optical response calculations using different gauges and methods, identifying the most reliable approach.

Findings

Length gauge methods converge faster and are more accurate.

Velocity gauge methods exhibit unphysical divergences in truncated models.

Length gauge calculations eliminate low-frequency divergences.

Abstract

We study the effects of a truncated band structure on the linear and nonlinear optical response of crystals using four methods. These are constructed by (i) choosing either length or velocity gauge for the perturbation and (ii) computing the current density either directly or via the time-derivative of the polarization density. In the infinite band limit, the results of all four methods are identical, but basis truncation breaks their equivalence. In particular, certain response functions vanish identically and unphysical low-frequency divergences are observed for few-band models in the velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study, we analyze the problems associated with all methods and identify the optimal one. Our results show that the length gauge calculations provide the fastest convergence rates as well as the most accurate spectra for any basis size and, moreover, that low-frequency divergences are eliminated.