Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

TL;DR

This paper uncovers a hidden symmetry in bipartite lattice superconductors that leads to universal relations for pairing and superfluid weight, unaffected by disorder, with implications for flat band high-temperature superconductivity.

Contribution

It reveals a hidden symmetry in Bogoliubov de Gennes eigenstates of bipartite lattices, establishing universal, disorder-insensitive relations in flat band superconductors.

Findings

Universal relations for pairing and superfluid weight are derived.

These relations are independent of hopping details.

Properties remain robust under disorder as long as bipartite symmetry is preserved.

Abstract

Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T$_c$ materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.