Disorder and the Robustness of Superconductivity on the Flat Band

TL;DR

This study demonstrates that flat band superconductivity on the Creutz lattice is resilient to disorder, with a finite critical disorder strength needed to localize pairs and destroy superconductivity, confirmed through large-scale simulations.

Contribution

It reveals the robustness of flat band superconductivity against disorder and characterizes the disorder-induced transition as a Berezinskii-Kosterlitz-Thouless type.

Findings

Critical disorder strength $W_c$ is finite for all interaction strengths.

Superconducting transition is of the BKT type.

Localization at small interactions is due to pair localization, not single fermions.

Abstract

We study the interplay between on-site disorder and fermion pairing on the quasi one-dimensional flat band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat band superconductivity is robust against disorder: The critical disorder strength, $W_c$, required to localize the fermion pairs and destroy superconductivity, is finite at any interaction strength, $U$, and is proportional to the superconducting weight, $D_s$, of the clean system. Using large scale density matrix renormalization group computations, we show that this transition is of the BKT form. In addition, even at very small interaction strength, the localization is not due to single fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that $W_c$ can be accurately determined by using an appropriate scaling function.