Quantum Monte Carlo study of a magnetic-field-driven 2D   superconductor-insulator transition
  We numerically study the superconductor-insulator phase transition in a model disordered 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(\theta_i-\theta_j-A_{ij}), where A_{ij} has a mean of zero and a standard deviation \Delta A_{ij}. 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 \Delta A_{ij} then corresponds to an applied field such that the average number of flux quanta per plaquette has various integer values N: larger N corresponds to larger \Delta A_{ij}. For any value of \Delta A_{ij}, there appears to be a critical coupling constant K_c(\Delta A_{ij})=\sqrt{[J/(2U)]_c}, where U is the charging energy, above which the system is a Mott insulator; there is also a corresponding critical conductivity \sigma^*(\Delta A_{ij}) at the transition. For \Delta A_{ij}=\infty, 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 \Delta A_{ij} takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is z \sim 1.3. By contrast, z=1 for this model at \Delta A_{ij}=0. We suggest that the superconductor to insulator transition is actually of this I to BG class at all nonzero \Delta A_{ij}'s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion. 
Kwangmoo Kim, David Stroud