Interaction and coherence in 2D bilayers

TL;DR

This paper investigates interlayer coherence in 2D bilayers using Hartree-Fock theory, revealing phase diagrams, critical temperatures, and the effects of tunneling, and compares electron-electron and electron-hole bilayer systems.

Contribution

It provides a comprehensive theoretical analysis of interlayer coherence in 2D bilayers, highlighting differences and similarities between e-e and e-h systems within a unified framework.

Findings

Interlayer coherence signals spontaneous U(1) symmetry breaking.

Critical temperature in e-e bilayers is about one-third of that in excitonic condensates.

Weak interlayer tunneling influences the interlayer coherence order parameter.

Abstract

In bilayer systems, the additional layer pseudospin enables the emergence of interlayer coherence (IC), which is a direct consequence of the interlayer Coulomb interaction. This study presents a comprehensive HF investigation of IC in 2D bilayers, uncovering ground-state behaviors and temperature-dependent phase transitions that are distinct from single-layer 2DEG. This IC signals a spontaneous breaking of the U(1) symmetry in pseudospin. We explore the zero-temperature phase diagrams as a function of the electron density and interlayer separation within the HF formalism. We also calculate the critical temperature ($T_c$) of the interlayer coherence onset by self-consistently solving the HF gap-like equation. We contrast this IC phase in e-e bilayers with the closely related excitonic superfluid phase in e-h bilayers. Though both e-e and e-h bilayers spontaneously break the pseudospin U(1) symmetry, e-h bilayers produce BCS-BEC crossover intrinsic to the excitons acting as effective bosons or Cooper pairs, whereas the symmetry-broken phase in e-e bilayers is akin to the XY or easy-plane pseudospin ferromagnetism. Using the same system parameters and a similar theoretical framework, we find that $T_c$ of the interlayer coherent phase in e-e bilayers is about one-third of that in exciton condensates, suggesting a weaker IC in e-e bilayers. In addition, we examine the effect of a weak interlayer tunneling on the IC order parameter, drawing parallels with the influence of an effective in-plane magnetic field on the XY pseudospin ferromagnetism. Our findings provide a comparative theoretical framework that bridges the gap between the IC physics in e-e and e-h bilayers, contributing to a unified understanding of phase transitions in low-dimensional electron/hole systems and establishing in particular the same universality class for interlayer phase coherence in both e-e and e-h bilayers.