Flat band superconductivity in a system with a tunable quantum metric : the stub lattice

TL;DR

This paper investigates flat band superconductivity in a one-dimensional stub lattice, revealing how tunable quantum metric influences superfluid weight and pairing, with detailed analysis across different coupling regimes and thermal effects.

Contribution

It introduces the study of flat band superconductivity in a stub lattice with tunable quantum metric, providing analytical and numerical insights into the interplay between quantum metric, pairing, and superfluid weight.

Findings

Superfluid weight D_s scales linearly with quantum metric for large ngle g ngle.

Unusual power law D_s  ngle g ngle^ u with  rrow 2 in large gap limit.

Thermal fluctuations impact superfluid weight, analyzed in the study.

Abstract

Over the past years, one witnesses a growing interest in flat band (FB) physics which has become a playground for exotic phenomena. In this study, we address the FB superconductivity in onedimensional stub chain. In contrast to the sawtooth chain or the creutz ladder, for a given strength of the attractive electron-electron interaction, the stub chain allows the tuning of the real space spreading of the FB eigenstates (quantum metric or QM). We study in detail the interplay between the interaction strength and the mean value of the QM \langle g \rangle on the pairings and on the superfluid weight D_s. Our calculations reveal several interesting and intriguing features. For instance, in the weak coupling regime, D_s with respect to \langle g \rangle exhibits two different types of behaviour. Despite the fact that the pairings differs drastically, D_s scales linearly with the QM only when its \langle g \rangle is large enough (small gap limit). On the other hand, when the QM is of small amplitude an unusual power law is found, more precisely D_s \propto \langle g \rangle^\nu where \nu \longrightarrow 2 in the limit of large single particle gap. In addition to the numerical calculations, we have provided several analytical results which shed light on the physics in both the weak and strong coupling regime. Finally, we have addressed the impact of the thermal fluctuations on the superfluid weight.