Robustness of flat-band superconductivity

In this study, we looked into the superfluid weight of disordered flat-band superconductors. Surprisingly, we found a universal suppression independent of the dispersion and the quantum geometry of the underlying energy bands.

The superfluid weight is a transport coefficient closely connected to a superconductor’s hallmark properties: the presence of dissipationless electric currents and the expulsion of magnetic fields from its interior, also known as the Meissner effect. Conventional superconductors arise from superconducting instabilities in metals with curved electronic energy bands. Here, the superfluid weight is connected to the band curvature: a large curvature translates into a large superfluid weight, whereas a small curvature leads only to a small superfluid weight. In particular, flat energy bands without any curvature are not expected to enable superconductivity because of a vanishing superfluid weight.

This is, however, not the full story: also flat electronic bands can lead to a large superfluid weight provided the involved electrons have a nontrivial quantum geometry, such as in topological bands. This gives rise to a geometric contribution to the superfluid weight. Topological bands are characterized by integer numbers, such as Chern numbers, and are inherently robust against small disorder.

For this work, we set out to answer the open question whether this robustness against disorder carries over also to superconductors derived from flat, topological bands. For this purpose, we compared different theoretical models with flat topological, curved topological, and conventional energy bands with respect to how the superfluid weight of their superconducting phases behaves in the presence of disorder.

We found that all considered superconductors show the same universal behaviour: the superfluid weight is suppressed by disorder in a way independent of the band curvature and, in particular, independent of the quantum geometry of the underlying electronic bands. At the same time, this also means that flat-band superconductors are as resilient to disorder as conventional superconductors: the flatness of their bands does not make them more prone to losing their superconducting properties. Our theoretical predictions are immediately relevant  to experimental studies, for instance in graphene-based heterostructures, which have a high degree of tunability and are known to realize various superconducting phases.

A. Lau, S. Peotta, D. I. Pikulin, E. Rossi, and T. Hyart,
Universal suppression of superfluid weight by non-magnetic disorder in s-wave superconductors independent of quantum geometry and band dispersion,
SciPost Physics 13, 086 (2022), arXiv:2203.01058