Quantum Monte Carlo study of a magnetic-field-driven 2D superconductor-insulator transition

Abstract

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(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 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 ΔA_{ij}. For any value of ΔA_{ij}, there appears to be a critical coupling constant K_c(ΔA_{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 σ^*(ΔA_{ij}) at the transition. For ΔA_{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 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 \sim 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.

17 pages, 23 figures, accepted for publication in Phys. Rev. B

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• Magnetic flux disorder and superconductor-insulator transition in nanohole thin films
• Quantum decay of the persistent current in a Josephson junction ring
• Disorder-induced superconductor to insulator transition and finite phase stiffness in two-dimensional phase-glass models
• Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors
• Magnetic field-dependent inhomogeneities and their effect on the magnetoresponse of 2D superconductors
• FFLO oscillations and magnetic domains in the Hubbard model with off-diagonal Coulomb repulsion
• Superconductor to Insulator Transition Tuned by Random Gauge Fields
• Persistent current in a 2D Josephson junction array wrapped around a cylinder