The two-gap BCS model in the large-N approximation within a field-theory approach

Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará - C.P. 66075-110, Belém, PA, Brazil

^(a) E-mail: lon@ufpa.br (corresponding author)

Received: 5 October 2022
Accepted: 31 January 2023

Abstract

We study the continuum version of the two-gap BCS model in (3 + 1)D within the large-N approximation. We calculate the effective potential of the model which depends on two independent energy gaps σ and Δ, where σ describes the Cooper pair made of electrons that belong to the same internal symmetry whereas Δ describes the Cooper pair of electrons that have a different internal symmetry. The effective potential is calculated by considering that the Debye frequency is an ultraviolet cutoff Λ, which is meant to describe the physical lattice of 3D superconductors. Our main result shows that the extra gap provides a possible inter-band phase transition that may be either a stable or metastable phase, depending on the competion between the coupling constants of the model. We also derive the critical temperature below which the phases may be observed.