Ultrarelativistic electron-hole pairing in graphene bilayer

TL;DR

This paper investigates the ground state and electron-hole pairing mechanisms in graphene bilayers, revealing a transition from BCS-like behavior to ultrarelativistic effects at strong coupling, with implications for gap magnitude.

Contribution

It introduces a detailed analysis of electron-hole pairing in graphene bilayers, highlighting the impact of strong coupling and the ultrarelativistic electron dynamics on the pairing gaps.

Findings

Weak coupling regime resembles BCS condensate.

Strong coupling induces effects on remote bands.

Gap magnitude depends exponentially on pairing region width.

Abstract

We consider ground state of electron-hole graphene bilayer composed of two independently doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only conduction band of electron-doped layer and valence band of hole-doped layer, thus the ground state is similar to ordinary BCS condensate. At strong coupling, an ultrarelativistic character of electron dynamics reveals and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. The analysis of instability of unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. A relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of separable potential. It is shown that, if characteristic width of the pairing region is of the order of magnitude of chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However, if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.