# Discrete Interactions between a few Interlayer Excitons Trapped at a MoSe$_2$-WSe$_2$ Heterointerface

## TL;DR

This study investigates the interactions of a few interlayer excitons confined at a heterointerface in TMD bilayers, revealing discrete multiparticle states and quantifying their dipolar and exchange interactions, advancing understanding of quantum correlations in 2D systems.

## Contribution

It provides the first detailed experimental measurement of discrete multiparticle interlayer exciton states and their interactions in a nanoscale confined TMD heterobilayer.

## Key findings

- Observation of discrete multiparticle exciton states with N_{IX}~1-5.
- Measurement of interlayer biexciton energy splitting and exchange interactions.
- Numerical modeling supports the experimental confinement lengthscale of ~3 nm.

## Abstract

Interlayer excitons (IXs) in hetero-bilayers of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The long-range interactions that arise from the spatial separation of electrons and holes can give rise to novel quantum, as well as classical multi-particle correlation effects. In order to acquire a detailed understanding of the possible many-body effects, the fundamental interactions between individual IXs have to be studied. Here, we trap a tunable number of dipolar within a nanoscale confinement potential induced by placing a MoSe$_2$-WSe$_2$ hetero-bilayer (HBL) onto an array of SiO$_2$ nanopillars. We control the mean occupation of the IX trap via the optical excitation level and observe discrete sharp-line emission from different configurations of interacting IXs. We identify these features as different multiparticle states with $N_{IX}\sim1-5$ via their power dependencies and directly measure the hierarchy of dipolar and exchange interactions as $N_{IX}$ increases. The interlayer biexciton ($N_{IX}=2$) is found to be an emission doublet that is blue-shifted from the single exciton by $\Delta E=(8.4\pm0.6)$ meV and split by $2J=(1.2\pm0.5)$ meV. The blueshift is even more pronounced for triexcitons ($(12.4\pm0.4)$ meV), quadexcitons ($(15.5\pm0.6)$ meV) and quintexcitons ($(18.2\pm0.8)$ meV). These values are shown to be mutually consistent with numerical modelling of dipolar excitons confined to a harmonic trapping potential having a confinement lengthscale in the range $\ell\approx 3$ nm. Our results contribute to the understanding of interactions between IXs in TMD HBLs at the discrete limit of only a few excitations and represent a key step towards exploring quantum correlations between them.