Artificial flat bands in frustrated Josephson junction arrays based on a superconductor/semiconductor hybrid platform

Epitaxial semiconductor-superconductor hybrid materials provide a novel highly-tunable platform to study exotic emergent quantum phenomena, taking advantage of gate-controlled density, ballistic transport, and non-sinusoidal current-phase relations. Recently, hybrid Josephson junction arrays have been used to study a gate-controlled superconductor-insulator transition (SIT), where Josephson coupling between Islands, E_J, can be tuned to be greater than or less than the charging energy of the island, E_C.

When applying a perpendicular magnetic field, frustration is introduced, leading to complex ground states, which depend on the geometry of the array. I will present data recorded in a two-dimensional Josephson junction array with dice lattice geometry, which is predicted to host flat bands when frustrated. I will discuss our recent effort to map out the phase diagram as a function of frustration. Commensurate values of frustration lead to the formation of vortex lattices, which are absent at incommensurate values of frustration. When frustrating the array with half a flux quantum per array plaquette, quantum interference localizes individual Cooper pairs on the array, corresponding to formation of a flat band system.