Excitons in fractionally-filled moir\'{e} superlattices

TL;DR

This paper develops a theoretical model to explain exciton behavior in fractionally-filled moiré superlattices, linking exciton absorption shifts to charge ordering and providing insights into correlated insulating states observed experimentally.

Contribution

The paper introduces a theory connecting exciton absorption features to charge order in fractional moiré superlattices, explaining experimental observations of correlated insulating states.

Findings

Exciton energy shifts indicate charge ordering in the superlattice.

Differences in exciton resonance shifts depend on site occupancy.

The theory supports electrons forming a Wigner crystal at fractional fillings.

Abstract

Long-range Coulomb forces give rise to correlated insulating states when charge particles populate a moir\'{e} superlattice at certain fractional filling factors. Such behavior is characterized by a broken translation symmetry wherein particles spontaneously form a Wigner crystal. Focusing on the experimental findings of Xu et al. [Nature \textbf{587}, 214 (2020)], we present a theory that captures the correlated insulating state of a fractionally-filled moir\'{e} superlattice through the energy shift and change in oscillator strength of the exciton absorption resonance. The theory shows that the experimental findings can only be supported if the electrons reside in a charge-ordered state (i.e., electrons are not randomly distributed among the sites of the moir\'{e} superlattice). Furthermore, we explain why the energy shifts of exciton resonances are qualitatively different in cases that the superlattice is nearly empty compared with a superlattice whose sites are doubly occupied.