# Exciton Condensate Modulation in Electron-Hole Bilayers: A Real-Space Visualization

## TL;DR

This paper investigates how exciton condensates in electron-hole bilayers change with density polarization, revealing phase transitions and modulated states, and visualizes these phenomena through real-space modeling.

## Contribution

It introduces a real-space mean-field model to visualize exciton condensate textures and identifies phase transitions and modulated states with varying density polarization.

## Key findings

- Phase transitions from superfluid to normal state with increased polarization
- Identification of stripe-like and modulated exciton states
- Observation of intra-gap resonance quasiparticle states

## Abstract

We study the texture of the exciton condensate at low temperatures in an independently gated electron-hole bilayer system. A model Hamiltonian is solved in real space within a mean-field approximation. It is found that, with increased electron-hole density polarization, the system experiences phase transformations from the zero center-of-mass momentum superfluid state, through one- and two-dimensional exciton pair modulated states, into the normal state. At weak density polarization, the modulating state resembles the Larkin-Ovchinikov state in superconductors in the presence of an exchange field in the weak-coupling BCS limit, and becomes stripe-like in the strong coupling BEC limit. In the one-dimensional modulated phase, the density of states exhibits low-energy intra-gap resonance quasiparticle states, which are localized in the nodal region.