Strong-coupling theory of condensate-mediated superconductivity in 2D materials

TL;DR

This paper develops a strong-coupling theory for condensate-mediated superconductivity in 2D materials, deriving Eliashberg equations and estimating critical temperatures influenced by bogolon interactions.

Contribution

It introduces a comprehensive strong-coupling framework for superconductivity mediated by bogolons in 2D electron systems near exciton condensates, including new analytical expressions and temperature estimates.

Findings

Superconducting critical temperature depends linearly on coupling strength.

Bogolon-pair-mediated interaction dominates electron pairing in the system.

Critical temperature varies with exciton condensate density.

Abstract

We develop a strong-coupling theory of Bose-Einstein condensate-mediated superconductivity in a hybrid system, which consists of a two-dimensional electron gas with either (i) parabolic spectrum or (ii) relativistic Dirac spectrum in the vicinity of a two-dimensional solid-state condensate of indirect excitons. The Eliashberg equations are derived and the expressions for the electron pairing self-energy due to the exchange interaction between electrons mediated by a single Bogoliubov excitation (a bogolon) and the bogolon pairs are found. Furthermore, we find the superconducting order parameter and estimate the critical temperature of the superconducting transition. The critical temperature reveals its linear dependence on the dimensionless coupling constant. It is shown, that the bogolon-pair-mediated interaction is the dominant mechanism of electron pairing in hybrid systems in both the weak and strong coupling regimes. We calculate the effective bogolon-electron interaction constant for both parabolic and linear electron dispersions and examine the dependence of the critical temperature of electron gas superconducting transition on exciton condensate density.