Interaction-Enhanced Coherence Between Two-Dimensional Dirac Layers

TL;DR

This paper investigates how strong Coulomb interactions can induce a significant excitonic gap and phase transition in coupled two-dimensional Dirac materials like graphene and topological insulators, emphasizing the conditions for interlayer coherence.

Contribution

It provides a self-consistent analysis of interaction-induced coherence and excitonic gap formation in Dirac layers, revealing a first order phase transition dependent on interlayer separation and screening effects.

Findings

Excitonic gap can reach the order of the Fermi energy at strong interactions.

The phase transition between incoherent and coherent phases is first order.

Interlayer coherence requires small separation and negligible extrinsic screening.

Abstract

We estimate the strength of interaction-enhanced coherence between two graphene or topological insulator surface-state layers by solving imaginary-axis gap equations in the random phase approximation. Using a self-consistent treatment of dynamic screening of Coulomb interactions in the gapped phase, we show that the excitonic gap can reach values on the order of the Fermi energy at strong interactions. The gap is discontinuous as a function of interlayer separation and effective fine structure constant, revealing a first order phase transition between effectively incoherent and interlayer coherent phases. To achieve the regime of strong coherence the interlayer separation must be smaller than the Fermi wavelength, and the extrinsic screening of the medium embedding the Dirac layers must be negligible. In the case of a graphene double-layer we comment on the supportive role of the remote $\pi$-bands neglected in the two-band Dirac model.