Bosonic fractional quantum Hall effect in pattered hybrid lattices

Forty years after its discovery, the fractional quantum Hall (FQH) effect continues to be one of the most active research areas in mesoscopic quantum physics, including the Nobel prize in 1998. Each of the emerging FQH states is described by a different topological order with unique anyonic quasiparticle excitations. So far, the FQH excitations have mostly been studied in ultra-pure two-dimensional electron gas (2DEG) through interferometry or other sophisticated transport techniques. Despite the great theoretical and experimental effort, the realization of topologically ordered states has proved to be challenging. Here, we propose a radically different approach to demonstrating FQH states, based on artificially fabricated model systems: frustrated Josephson-junction arrays (JJAs). The idea relies on networks of weakly-coupled superconducting islands fabricated on semiconducting substrates allowing gate-voltage control of both Josephson, EJ, and charging, EC, energies. At the same time, it does not require exceptionally high-quality materials or very large magnetic fields. The reason why this has not been realized before is that the conventional all-metallic JJAs do not allow for the required controllability. This fundamentally different approach offers a novel path for the controlled study of FQH states and gives a fresh perspective to the problem.