Relativistic BCS Theory in Quasi-(2+1)-Dimensions: Effects of an Inter-layer Transfer in the Honeycomb Lattice Symmetry

TL;DR

This paper investigates relativistic BCS superconductivity in a quasi-(2+1)-dimensional system, focusing on how inter-layer transfer, chemical potential, and mass parameters influence the superconducting gap in graphene-like materials.

Contribution

It introduces a relativistic BCS model incorporating inter-layer transfer effects in a quasi-(2+1)-dimensional honeycomb lattice, extending previous non-relativistic theories.

Findings

Inter-layer transfer parameter $t$ significantly affects the superconducting gap.

Chemical potential $$ influences the gap and phase structure.

Mass parameter $m$ opens a gap at the Dirac point, modifying superconducting properties.

Abstract

Motivated by recent huge interests on graphene sheet and graphite as "relativistic" systems, a BCS superconductivity in a quasi-(2+1)-dimensional relativistic model is investigated. The intra-layer particle dynamics is described by a (2+1)-dimensional Gross-Neveu-type four-body contact interaction model, while inter-layer particle motions will be caused by a hopping term with a transfer parameter $t$. Especially, we examine the effects of non-vanishing $t$, chemical potential $\mu$, and a mass parameter $m$ which will give a gap at a conical intersection point of the relativistic band dispersion, in the BCS s-wave (scalar) superconducting gap function $\Delta$.