Superconductor-insulator transition in nanowires and nanowire arrays

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip (QPS) processes replacing the tunneling of Cooper pairs. When the QPS amplitude E_S is much smaller than the inductive energy E_L, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of E_S/E_L is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of E_S/E_L. They can be tuned by a homogeneous magnetic frustration.