Excitons in periodic potentials

TL;DR

This paper investigates the energy band structure of excitons in periodic potentials, revealing how their optical properties and energy shifts relate to electron arrangements in monolayer semiconductors.

Contribution

It introduces a simplified one-body model for excitons in periodic potentials and uses group theory to analyze their optical coupling and energy shifts.

Findings

Identifies excitonic energy bands that couple to light.

Quantifies energy shifts with potential period changes.

Links electron order in Wigner crystals to exciton blueshift.

Abstract

The energy band structure of excitons is studied in periodic potentials produced by the short-range interaction between the exciton and electrons of Wigner or Moir\'{e} lattices. Treating the exciton as a point-like dipole that interacts with the periodic potential, we can solve a simple one-body problem that provides valuable information on excitons in many-body problem settings. By employing group theory, we identify the excitonic energy bands that can couple to light and then quantify their energy shifts in response to a change in the period of the potential. This approach allows us to emulate the response of optically active exciton and trion states to a change in electron density. We gain important insights on the relation between the electron order in a Wigner crystal and the energy blueshift of the bright exciton. We discuss the consequences of this relation in the context of optical absorption experiments in monolayer semiconductors.