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 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 it highlights the importance of the Berry curvature in the effective mass approximation.
Highlights
The effective mass approximation provides a simple yet extremely useful tool to understand a wide variety of electronic properties of semiconductors [1]
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 k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function
Summary
Quite generally, the Berry curvature modifies the effective Hamiltonian for excitons, and causes an energy splitting between exciton states with opposite angular momentum This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. We confirm this result by a detailed study of the massive Dirac fermion model in two dimensions, and show that the energy splitting can be understood as an effective spin-orbit coupling effect.
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