Quantum Monte Carlo Study of a Magnetic-Field-Driven 2D Superconductor-Insulator Transition

Using quantum Monte Carlo calculations of the $(2+1)$D $XY$ model, we study the superconductor-insulator phase transition of a disordered 2D superconducting film vs. the applied magnetic field. The $XY$ coupling is assumed to be $-J\cos(\theta_i-\theta_j-A_{ij})$, where $A_{ij}$ has a standard deviation $\Delta A_{ij}$. The critical coupling constant $K_{c} = \sqrt{[J/(2U)]_c}$ and the universal conductivity $\sigma^{*}$ are found to increase monotonically with $\Delta A_{ij}$. Beyond a certain critical value of $\Delta A_{ij}$, the superfluid density vanishes for all $K$'s, but a renormalized coupling constant $g$ remains finite, suggesting a transition into a Bose glass phase. At a larger value of $\Delta A_{ij}$, the system becomes a Mott insulator. The critical values are found to be $K_{c}=0.490\pm 0.001$ and $\sigma^{*}/\sigma_{Q}=0.324\pm 0.003$ when $\Delta A_{ij}=1/2$; $K_{c}=0.532\pm 0.001$ and $\sigma^{*}/\sigma_{Q}=0.494\pm 0.011$ when $\Delta A_{ij}=1/\sqrt{2}$; $K_{c}=0.585\pm 0.004$ when $\Delta A_{ij}=0.854$; and $K_{c}=0.630\pm 0.002$ when $\Delta A_{ij}=\infty$. The last value, which represents a Bose glass to Mott insulator transition, is obtained from $g$, whereas the others represent a superconductor-to-insulator transition and are obtained from the superfluid density. We conclude that, for certain couplings, a disordered film may undergo a transition from superconductor to Bose glass to insulator with increasing field.