Excitonic condensation of massless fermions in graphene bilayers

TL;DR

This paper explores the formation of an excitonic condensate in graphene bilayers with massless carriers, revealing a large phase stability range and specific dependencies of excitonic properties on carrier density.

Contribution

It provides a mean-field theoretical analysis of excitonic condensation in graphene bilayers, including the phase diagram, gap, and quasiparticle properties, highlighting the behavior of massless excitons.

Findings

Uniform excitonic condensate exists over a wide density range.

Condensate phase stiffness and exciton mass scale with the square root of carrier density.

The condensate is predicted not to undergo Wigner crystallization.

Abstract

Graphene, a single sheet of graphite with honeycomb lattice structure, has massless carriers with tunable density and polarity. We investigate the ground state phase diagram of two graphene sheets (embedded in a dielectric) separated by distance $d$ where the top layer has electrons and the bottom layer has holes, using mean-field theory. We find that a uniform excitonic condensate occurs over a large range of carrier densities and is weakly dependent on the relative orientation of the two sheets. We obtain the excitonic gap, quasiparticle energy and the density of states. We show that both, the condensate phase stiffness and the mass of the excitons, with massless particles as constituents, vary as the square-root of the carrier density, and predict that the condensate will not undergo Wigner crystallization.