Interaction-enhanced coherence between two-dimensional Dirac layers

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 π-bands neglected in the two-band Dirac model.

Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene

“…In QCD with gauge group SU(2) there is a so-called quarkyonic regime above onset where ∝ μ 2 [16]; this is consistent with degenerate fermions in 3 + 1d with a gap ∼ O( QCD ) independent of μ. It is also very different from the result /μ ∼ O(10 −7 ) obtained by self-consistent diagrammatic techniques [7], although comparable with the large values of /μ obtained in [5], where it was found that depends sensitively on the treatment of screening effects, and in particular on the reduction of screening once the superfluid gap forms. One feature of our approach which does merit comparison with the treatment in [5] is that competition between inter-and intralayer pairing condensates can be addressed; see Fig.…”

“…Although V defined in this way yields a potential with no classical Coulomb r −1 tail, it was shown in [6] that V and A 0 in (1) have the same large-N f quantum corrections, and the models coincide in the strong coupling limit e 2 ,g 2 → ∞. Because some weak interlayer hybridization is likely to be present in double-layer systems, in general j = 0 [5]; however we will attempt to extrapolate j → 0 so that exciton condensation can be viewed as a spontaneous symmetry breaking U (4) ⊗ U (4) → U (4) [1]. In continuum notation the covariant derivative operator including the bias voltage is…”

“…the essential features of a more general model for doublelayer graphene systems in which there is some hybridization permitting interlayer tunneling [5]. With N f = 1 this approach is also applicable to surface states of topological insulators, motivating study with variable N f [6].…”

“…They find a very small value /μ ∼ e −4N f ∼ O(10 −7 ). Sodemann et al [5] take the ω dependence of into account, thereby modeling the retarded character of the polarization induced by relativistic degrees of freedom, and find a significant reduction of screening as q,ω → 0 in a gapped phase with > 0. They find /μ ∼ O(1) for values of the effective fine structure constant α = e 2 /εv F > α c ∼ 1.5.…”

“…The minimal coupling to V implies that ψψ, φφ, and φψ interactions are all of equal strength, which is required for the action to be real following integration over the fermions. This corresponds to the interlayer separation d → 0 in the double-layer model [5].…”