Flat-band superconductivity in a system with a tunable quantum metric: The stub lattice
M. Thumin, G. Bouzerar
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 one-dimensional 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 $\ensuremath{\langle}g\ensuremath{\rangle}$ 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 $\ensuremath{\langle}g\ensuremath{\rangle},$ exhibits two different types of behavior. Despite the fact that the pairings differs drastically, ${D}_{s}$ scales linearly with the QM only when its $\ensuremath{\langle}g\ensuremath{\rangle}$ 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 ${D}_{s}\ensuremath{\propto}{\ensuremath{\langle}g\ensuremath{\rangle}}^{\ensuremath{\nu}}$, where $\ensuremath{\nu}\ensuremath{\rightarrow}2$ 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.