Exotic Superconductivity Through Bosons in a Dynamical Cluster Approximation

TL;DR

This study investigates how mixtures of spin-1/2 fermions and scalar bosons on a 2D lattice can exhibit exotic superconductivity, with findings suggesting high critical temperatures for d-wave pairing, relevant for cold atom experiments.

Contribution

It demonstrates the emergence of d-wave superconductivity mediated by bosons using the Dynamical Cluster Approximation with a continuous-time Monte Carlo solver.

Findings

d-wave superconductivity can be stable with boson-mediated interactions

Critical temperature for d-wave pairing can match that of s-wave

Potential for experimental detection in cold atom systems

Abstract

We study the instabilities towards (exotic) superconductivity of mixtures of spin-$1/2$ fermions coupled to scalar bosons on a two-dimensional square lattice with the Dynamical-Cluster-Approximation (DCA) using a numerically exact continuous-time Monte-Carlo solver. The Bogoliubov bosons provide an effective phononic bath for the fermions and induce a non-local retarded interaction between the fermions, which can lead to (exotic) superconductivity. Because of the sign problem the biggest clusters we can study are limited to $2 \times 2$ in size, but this nevertheless allows us to study the pairing instablilities, and their possible divergence, in the $s$- and $d$ -wave channels as well as the competition with antiferromagnetic fluctuations. At fermionic half-filling we find that $d$-wave is stable when the mediated interaction by the bosons is of the same order as the bare fermionic repulsion. Its critical temperature can be made as high as the maximum one for $s$-wave, which opens perspectives for its detection in a cold atom experiment.