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We study numerically the superconductor to insulator transition intwo-dimensional phase-glass (or chiral-glass) models with varying degree ofdisorder. These models describe the effects of gauge disorder insuperconductors due to random negative Josephson-junction couplings, or $\pi$junctions. Two different models are considered, with binary and Gaussiandistribution of quenched disorder, having nonzero mean. Monte Carlo simulationsin the path-integral representation are used to determine the phase diagram andcritical exponents. In addition to the usual superconducting and insulatingphases, a chiral-glass phase occurs for sufficiently large disorder, withrandom local circulating currents of different chiralities. A transition fromsuperconductor to insulator can take place via the intermediate chiral-glassphase. We find, however, that the chiral-glass state has a finite phasestiffness, being still a superconductor, instead of the Bose metal, which hasbeen suggested by mean-field theory.

Disorder-induced superconductor to insulator transition and finite phase stiffness in two-dimensional phase-glass models