Alternating superconductor-insulator transport characteristics in a quantum vortex chain

Experimental studies of magnetoresistance in thin superconducting strips subject to a perpendicular magnetic field B exhibit a multitude of transitions, from superconductor to insulator and vice versa. Motivated by this observation, we study a theoretical model for the transport properties of a ladderlike superconducting device close to a superconductor-insulator transition. In this regime, strong quantum fluctuations dominate the dynamics of the vortex chain forming along the device. Utilizing a mapping of the vortex system at low energies to one-dimensional fermions at a chemical potential dictated by B, we find that a quantum phase transition of the Ising type occurs at critical values of the vortex filling, from a superconducting phase near integer filling to an insulator near half filling. The current-voltage (I-V) characteristics of the weakly disordered device in the presence of a d.c. current bias I is evaluated, and investigated as a function of B, I, the temperature T, and the disorder strength. In the Ohmic regime (I/eT), the resulting magnetoresistance R(B) exhibits oscillations similar to the experimental observation. More generally, we find that the I-V characteristics of the system manifests a dramatically distinct behavior in the superconducting and insulating regimes.