Berry phase modification to the energy spectrum of excitons

TL;DR

This paper demonstrates how Berry curvature influences the energy spectrum of excitons, causing splitting and shifts that challenge traditional hydrogenic models and highlight the role of topological effects in exciton physics.

Contribution

It introduces a semiclassical quantization approach showing Berry curvature causes energy splitting in excitons, revealing limitations of the hydrogenic model and emphasizing topological effects.

Findings

Berry curvature causes energy splitting between exciton states with opposite angular momentum.

The splitting is related to the Berry curvature flux in k-space.

Energy shifts are influenced by relativistic terms in the model.

Abstract

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the $\bm k$-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and highlights the importance of the Berry curvature in the effective mass approximation.