Generalized Wilson Loop Method for Nonlinear Light-Matter Interaction

TL;DR

This paper introduces a gauge-invariant generalized Wilson loop method for efficient, direct calculation of nonlinear optical responses, overcoming traditional computational challenges and providing geometric insights into light-matter interactions.

Contribution

The paper presents a novel Wilson loop-based approach for nonlinear optical response calculations that is gauge-invariant, efficient, and offers geometric interpretation, improving upon sum-over-states methods.

Findings

Avoids divergence at band degeneracy and optical zeros

Enables efficient and straightforward calculations

Provides geometric interpretation of nonlinear responses

Abstract

Nonlinear light-matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical methods with the sum-over-states approach. However, this indirect method often suffers from the divergence at band degeneracy and optical zeros as well as convergence issues and high computation costs when summing over the states. Here, using shift vector and shift current conductivity tensor as an example, we present a gauge-invariant generalized approach for efficient and direct calculations of nonlinear optical responses by representing interband Berry curvature, quantum metric, and shift vector in a generalized Wilson loop. This generalized Wilson loop method avoids the above cumbersome challenges and allows for easy implementation and efficient calculations. More importantly, the Wilson loop representation provides a succinct geometric interpretation of nonlinear optical processes and responses based on quantum geometric tensors and quantum geometric potentials and can be readily applied to studying other excited-state responses.