# Attraction of indirect excitons in van der Waals heterostructures with three semiconducting layers

## TL;DR

This paper investigates how indirect excitons form and behave in a symmetric three-layer TMD heterostructure, revealing a first-order charging transition, antiferroelectric ordering, and optical properties like red-shifted luminescence.

## Contribution

It introduces a theoretical model of indirect exciton behavior in three-layer heterostructures, highlighting a first-order charge transition and antiferroelectric exciton droplet formation.

## Key findings

- Charge enters the device at a critical voltage below the single-pair threshold.
- Differential capacitance becomes infinite at the critical voltage.
- Optical excitation leads to red-shifted luminescence due to exciton attraction.

## Abstract

We study a capacitor made of three monolayers of transition metal dichalcogenide (TMD) separated by hexagonal Boron Nitride (hBN). We assume that the structure is symmetric with respect to the central layer plane. The symmetry includes the contacts: if the central layer is contacted by the negative electrode, both external layers are contacted by the positive one. As a result a strong enough voltage $V$ induces electron-hole dipoles (indirect excitons) pointing towards one of the external layers. Antiparallel dipoles attract each other at large distances. Thus, the dipoles alternate in the central plane forming a 2D antiferroelectric with negative binding energy per dipole. The charging of a three-layer device is a first order transition, and we show that if $V_1$ is the critical voltage required to create a single electron-hole pair and charge this capacitor by $e$, the macroscopic charge $Q_c = eSn_c$ ($S$ is the device area) enters the three-layer capacitor at a smaller critical voltage $V_{c} < V_{1}$. In other words, the differential capacitance $C(V)$ is infinite at $V = V_{c}$. We also show that in a contact-less three-layer device, where the chemically different central layer has lower conduction and valence bands, optical excitation creates indirect excitons which attract each other, and therefore form antiferroelectric exciton droplets. Thus, the indirect exciton luminescence is red shifted compared to a two-layer device.