Quantum Criticality and Superconductivity in Quasi-Two-Dimensional Dirac Electronic Systems

TL;DR

This paper develops a theory for superconductivity in quasi-two-dimensional Dirac electron systems, revealing a quantum phase transition at zero temperature and suggesting relevance to high-Tc cuprate superconductors.

Contribution

It introduces a comprehensive model for Dirac electron superconductivity, analyzing phase transitions and the effects of physical cutoffs, with implications for high-Tc superconductivity mechanisms.

Findings

Quantum phase transition at critical coupling

Superconducting gap determined at T=0 and T≠0

Qualitative reproduction of underdoped cuprate phase transition

Abstract

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T=0 and T\neq 0, in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T=0, we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T=0 and T\neq 0, both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity.