Coherence length and quantum geometry in a dilute flat-band superconductor

TL;DR

This paper investigates how quantum geometric effects influence the coherence length in a dilute flat-band superconductor using a BCS-BEC crossover approach, revealing a monotonic decay of coherence length and similar effective masses for pairs.

Contribution

It introduces a self-consistent method to analyze quantum-geometric effects on coherence length in a multiband superconductor near the critical temperature.

Findings

Coherence length decreases monotonically with increasing interaction strength.

Effective mass of Cooper pairs matches that of two-body bound states in the dilute flat-band limit.

The approach benchmarks well against zero-temperature coherence length measurements.

Abstract

To explore the influence of quantum-geometric effects on the Ginzburg-Landau coherence length in a dilute flat-band superconductor, we adopt a BCS-BEC crossover approach to the multiband pyrochlore-Hubbard model near the critical temperature for superconductivity. Our self-consistent formulation for this three-dimensional lattice benchmarks very well against the so-called zero-temperature coherence length, demonstrating the monotonic decay of the coherence length to zero as the interaction strength increases. Additionally, we show that the effective mass of the many-body bound states (i.e., Cooper pairs) is nearly identical to that of the lowest-lying two-body bound states in the dilute flat-band limit.