Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids

TL;DR

This paper investigates how the quantum metric influences the effective mass of Cooper pairs in spin-orbit coupled Fermi superfluids, revealing its significant role across the BCS-BEC crossover.

Contribution

It derives a Ginzburg-Landau theory incorporating quantum metric effects and demonstrates their substantial impact on pair mass in superfluids.

Findings

Quantum metric significantly affects pair mass in superfluids.

The contribution is large across the BCS-BEC crossover.

Quantum metric influences superfluid density tensor.

Abstract

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature, and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum metric contribution accounts for a sizeable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-BEC crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables as well.