Fragile topology, strong superconductivity

Not all topological materials are the same. Recently, a new kind of topology dubbed "fragile" has been predicted in a myriad of materials and engineered structures. Magic-angle twisted bilayer graphene is surely a prominent example. These topological insulators do not display robust modes at their edges, and they can turn trivial by the addition of trivial degrees of freedom. What is then so interesting if nothing seems robust?

Fragile topology still prevents electrons from getting tightly localized. This feature becomes extremely important when single electrons are not able to move around on their own. If they overlap, they can feel each other and pair up to regain mobility and carry a supercurrent. This mechanism might explain the relatively high superconducting temperature measured in magic-angle twisted bilayer graphene. But is fragile topology important even when interactions get very strong?

Our study establishes via numerically exact techniques the importance of this novel topology even in the strong-coupling regime. Moreover, we find that as soon as the topological obstruction to localize is removed, the superconducting state gets suppressed. Our findings shed light in the thriving field of twisted two-dimensional quantum materials and the interplay between many-body physics and band topology.