Superconducting phase transition in planar fermionic models with Dirac cone tilting

TL;DR

This paper investigates how tilting the Dirac cone in a planar fermionic model affects chiral and superconducting gaps, revealing threshold-dependent behaviors and phase transitions influenced by tilt and chemical potential.

Contribution

It introduces the impact of Dirac cone tilting on superconducting and chiral phases, identifying a threshold tilt value that alters phase stability and gap induction mechanisms.

Findings

Superconducting phase persists for negative coupling when tilt is below threshold.

Chemical potential induces superconducting gaps similar to graphene systems.

Tilt influences phase boundaries and the emergence of metallic phases.

Abstract

The chiral and superconducting gaps are studied in the context of a planar fermion model with four-fermion interactions. The effect of the tilt of the Dirac cone on both gaps is shown and discussed. Our results point to two different behaviors exhibited by planar fermionic systems. We show that there is a threshold value $\tilde{t}^*$ for the effective tilt parameter such that when $|{\bf \tilde{t}}| < \tilde{t}^*$, the superconducting phase persists for negative values of the superconducting coupling constant. For positive values of the superconducting coupling constant, the induction of a superconducting gap by a chemical potential exists and which is similar to the one seen in graphene-like systems. For $|{\bf \tilde{t}}| > \tilde{t}^*$ and a negative superconducting coupling constant, the superconducting phase can be present, but it is restricted to a smaller area in the phase portrait. Our analysis also shows that when $|{\bf \tilde{t}}| > \tilde{t}^*$ and for positive values for the superconducting coupling constant, the induction of a superconducting gap in the presence of a chemical potential is ruled out. In this case, the increase of the chemical potential works in favor of the manifestation of a metallic phase.