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(θ_i−θ_j−A_ij), where A_ij has a mean of zero and a standard deviation ΔA_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 ΔA_ij 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 ΔA_ij. For any value of ΔA_ij, there appears to be a critical coupling constant K_c(ΔA_ij)=√[J/(2U)]_c, where U is the charging energy, below which the system is a Mott insulator; there is also a corresponding critical conductivity σ∗(ΔA_ij) at the transition. For ΔA_ij=∞, 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 ΔA_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∼1.3. By contrast, z=1 for this model at ΔA_ij=0. We suggest that the superconductor-to-insulator transition is actually of this I to BG class at all nonzero ΔA_ij’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)]. K_c is found to be a monotonically increasing function of ΔA_ij. For certain values of K, a disordered Josephson array may undergo a transition from an ordered, Bose glass phase to an insulator with increasing ΔA_ij