Signatures of Dimensionality and Symmetry in Exciton Bandstructure: Consequences for Time-Evolution

TL;DR

This paper develops a comprehensive theory of exciton bandstructure revealing non-analytical discontinuities caused by exchange scattering, which depend on material symmetry and dimensionality, impacting exciton dynamics and diffusion.

Contribution

It introduces a general theory showing exciton bandstructure features that differ from electronic bands, highlighting non-analytical discontinuities due to quantum exchange effects.

Findings

Discontinuities in exciton bandstructure depend on symmetry and dimensionality.

Exchange scattering causes non-analytical features absent in electronic bands.

Exciton bandstructure influences early-stage exciton dynamics and diffusion patterns.

Abstract

Exciton dynamics, lifetimes and scattering are directly related to the exciton dispersion, or bandstructure. While electron and phonon bandstructures are well understood and can be easily calculated from first principles, the exciton bandstructure is commonly conflated with the underlying electronic bandstructure, where the exciton dispersion is assumed to follow the same dispersion as the electron and hole bands from which it is composed (i.e., the effective mass model). Here, we present a general theory of exciton bandstructure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton bandstructure contains non-analytical discontinuities -- a feature which is impossible to obtain from the electronic bandstructure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D. We connect these unexpected features to the early stages of exciton dynamics, which shows remarkable correspondence with recent experimental observations and suggests that the measured diffusion patterns are influenced by the underlying exciton bandstructure.