# Electron-hole superfluidity controlled by a periodic potential

## TL;DR

This paper explores how an external periodic potential can be used to control electron-hole superfluidity in semiconductor quantum wells and 2D materials, analyzing phase transitions and pairing behavior.

## Contribution

It introduces a method to manipulate electron-hole superfluidity using periodic fields, including gate-induced and Moiré pattern effects, with a detailed mean-field analysis.

## Key findings

- Superfluidity can be tuned by external periodic potentials.
- A second order phase transition between superfluid and plasma states is identified.
- Dependence of pairing on temperature, density, and gate parameters is characterized.

## Abstract

We propose to control of an electron-hole superfluid in semiconductor coupled quantum wells and double layers of two-dimensional (2D) material by an external periodic field. This can either be created by the gates periodically located and attached to the quantum wells or double layers of 2D material or by the Moir\'e pattern of two twisted layers. The dependence of the electron-hole pairing order parameter on the temperature, the charge carrier density, and the gate parameters is obtained by minimization of the mean-field free energy. The second order phase transition between superfluid and electron-hole plasma, controlled by the external periodic gate field, is analyzed for different parameters.