Kitaev spin liquid in superconducting networks

Abstract

We propose a realization of the Kitaev honeycomb Hamiltonian -- an archetypal spin-liquid model -- in a superconducting metamaterial. The architecture consists of Cooper-pair boxes coupled through depleted semiconductor--superconductor heterostructures that do not require spin--orbit coupling. The Cooper-pair boxes encode effective spin degrees of freedom, while normal and anomalous virtual propagation through the heterostructures mediate bond-directional interactions. Two key control parameters are an out-of-plane magnetic flux and the semiconductor Fermi energy. The former controls interference and distinguishes the bond directions, while tuning the latter close to the bottom of the band gives rise to an emergent Nambu-exchange symmetry that enforces the required bond directionality. Through numerical calculations, we identify an operating regime with controlled corrections, with associated energy and length scales within experimental reach. These results establish a route toward equilibrium quantum spin liquids in engineered superconducting networks.