Relativistic BCS-BEC Crossover at Finite Temperature and Its Application to Color Superconductivity

TL;DR

This paper extends the non-relativistic BCS-BEC crossover theory to relativistic systems, revealing multiple crossovers and pseudogap phenomena relevant to color superconductivity at finite temperature.

Contribution

It develops a relativistic formalism for BCS-BEC crossover, incorporating uncondensed pairs and pseudogap effects, applicable to color superconductivity.

Findings

Existence of two crossovers with increasing coupling strength.

Pseudogap behavior similar to high-temperature superconductors.

Theory recovers non-relativistic and zero-temperature limits.

Abstract

The non-relativistic $G_0 G$ formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The uncondensed pairs contribute a pseudogap to the fermion excitations. The theory recovers the BCS mean field approximation at zero temperature and the non-relativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the non-relativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.