Adjoint computation of Berry phase gradients

TL;DR

This paper introduces an adjoint-based computational method to efficiently calculate gradients of Berry phases, facilitating the optimization of topological materials with desired wave transport properties.

Contribution

It presents a novel adjoint approach that simplifies Berry phase gradient computation, enabling advanced optimization in topological material design.

Findings

Efficient gradient computation with only one forward and one adjoint calculation.

Facilitates topology optimization for designing materials with specific topological properties.

Enhances control over wave propagation in topological materials.

Abstract

Berry phases offer a geometric perspective on wave propagation and are key to designing materials with topological wave transport. However, controlling Berry phases is challenging due to their dependence on global integrals over the Brillouin zone, making differentiation difficult. We present an adjoint-based method for efficiently computing the gradient of the Berry phase with respect to system parameters, involving only one forward and one adjoint calculation. This approach enables the use of advanced optimization techniques, such as topology optimization, to design new materials with tailored topological wave properties.