Quantum Monte Carlo study of a magnetic-field-driven two-dimensional superconductor-insulator transition

We numerically study the superconductor-insulator phase transition in a model disordered two-dimensional 2D superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the 2+1 D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form −J cos i− j −Aij , where Aij has a mean of zero and a standard deviation Aij. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values Aij then correspond to an applied field such that the average number of flux quanta per plaquette has various integer values N: larger N corresponds to larger Aij. For any value of Aij, there appears to be a critical coupling constant Kc Aij = J / 2U c, where U is the charging energy, below which the system is a Mott insulator; there is also a corresponding critical conductivity Aij at the transition. For Aij = , the order parameter of the transition is a renormalized coupling constant g. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of Aij takes place from an insulating I phase to a Bose glass BG phase, and that the dynamical critical exponent characterizing this transition is z 1.3. By contrast, z=1 for this model at Aij =0. We suggest that the superconductor-to-insulator transition is actually of this I to BG class at all nonzero Aij’s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion A. B. Harris, J. Phys. C 7, 1671 1974 . Kc is found to be a monotonically increasing function of Aij. For certain values of K, a disordered Josephson array may undergo a transition from an ordered, Bose glass phase to an insulator with increasing Aij.