Geometric Superfluid Weight in Quasicrystals

TL;DR

This paper introduces a flux-space quantum metric to analyze superfluidity in quasicrystals, revealing how quantum geometry influences superfluid weight despite the absence of translational symmetry.

Contribution

It develops a novel flux-space quantum metric framework for quasicrystals and links it to superfluid weight, extending quantum geometric analysis beyond periodic systems.

Findings

Flux-space quantum metric contributes to superfluid weight in quasicrystals.

Weak-coupling relation between superfluid weight and flux-space quantum metric established.

Quasiperiodicity modulates the quantum metric through Wannier function spread.

Abstract

We study the geometric contribution to the superfluidity in quasicrystals in which the conventional momentum-space quantum geometric tensor cannot be defined due to the lack of translational invariance. Based on the correspondence between the momentum and magnetic flux, we introduce the flux-space quantum metric in finite-size closed systems and reveal its contribution to the superfluid weight in quasicrystalline superconductors. As a toy model, we study the attractive Hubbard model on the Fibonacci quasiperiodic stub lattices that host flat energy spectra even in the presence of quasiperiodic hoppings. In the weak-coupling limit, we establish the relation between superfluid weight and the flux-space quantum metric in quasicrystal superconductors with flat energy spectra. Moreover, by analyzing the spread of Wannier functions, we propose a general fluctuation mechanism that explains how quasiperiodicity modulates the integrated flux-space quantum metric. Our theory provides a general way to examine the effect of the quantum geometry in systems lacking translational symmetry.