Exciton condensation and fractional charge in a bilayer two-dimension electron gas adjacent to a superconductor film

TL;DR

This paper investigates exciton condensates in a bilayer 2D electron gas near a superconductor with vortex lattices, revealing zero modes and fractional charges influenced by vortex profiles and chemical potentials.

Contribution

It introduces a theoretical and numerical analysis of exciton condensates with vortex profiles, uncovering fractional charge phenomena in a bilayer 2DEG system adjacent to a superconductor.

Findings

Exact zero modes with rational fractional charge at zero chemical potential.

Intervalley mixing causes irrational fractional axial charge when chemical potential is non-zero.

Vortex profiles in the order parameter lead to topologically protected zero modes.

Abstract

We study the exciton condensate (EC) in a bilayer two-dimension-electron-gas (2DEG) adjacent to a type-II superconductor thin film with an array of pinned vortex lattices. By applying continuum low energy theory and carrying numerical simulations of lattice model within mean-field approximation, we find that if the order parameter of EC has a vortex profile, there are exact zero modes and associated \emph{rational} fractional charge for zero pseudospin potential ($\mu$) and average chemical potential ($h$): $\mu$=0 and $h$=0; while for $\mu\mathtt{\neq}0$ and $h$=0, intervalley mixing splits the zero energy levels, and the system exhibits \emph{irrational} fractional \emph{axial} charge.