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

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 intralayer 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 µ, 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 ∆.

Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory

“…Since the global minimum point (GMP) of the TDP (21) coincides with the GMP either of the function ω 1 (M ) (22) or the function ω 2 (∆) (23), it is clear that in the chirally broken phase ∆ 0 = 0 and the gap M 0 does not depend on the parameter g 2 . Correspondingly, in the superconducting phase we have M 0 = 0 and the gap ∆ 0 does not depend on the parameter g 1 .…”

“…Among these systems are the high-T c cuprate and iron superconductors [13], the one-atom thick layer of carbon atoms, or graphene, [14,15] etc. Thus, many properties of such condensed matter systems can be explained in the framework of various (2+1)-dimensional QFT, including the GN-type models (see, e.g., [16][17][18][19][20][21][22][23][24] and references therein).…”

“…Starting from (C2) and taking into account the expression (23) for ω 2 (∆), we have the following gap equation:…”

Superconductivity Phenomenon Induced by External in-Plane Magnetic Field in (2 + 1)-Dimensional Gross–neveu Type Model

“…Among these systems are the high-T c cuprate and iron superconductors [27,28], the one-atom thick layer of carbon atoms, or graphene, [29,30] etc. Thus, many properties of such condensed matter systems can be explained in the framework of various (2+1)-dimensional QFT, including the GN-type models (see, e.g., [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and references therein).…”