Magnetic flux disorder and superconductor-insulator transition in nanohole thin films

We study the superconductor-insulator transition in nanohole ultrathin films in a transverse magnetic field by numerical simulation of a Josephson-junction array model. Geometrical disorder due to the random location of nanoholes in the film corresponds to random flux in the array model. Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, $f_o$. The resistivity increases with disorder for noninteger $f_o$ while it decreases for integer $f_o$, and reaches a common constant value in a vortex-glass regime above a critical value of the flux disorder $D_f^c$. The estimate of $D_f^c$ and the resistivity increase for noninteger $f_o$ are consistent with recent experiments on ultrathin superconducting films with positional disordered nanoholes.

Figure 1

Phase slippage response in (a) the imaginary-time direction $R_{\tau }$ and (c) spatial direction $R_x$ for $f_o=n+1/6$, near the transition. Flux-disorder strength $D_f=0.7$ and system size $L=60$. The couplings $g$ from the top down are $1.48, 1.47, 1.45, 1.44, 1.41, 1.39$, and $1.38$. (b) and (d) Scaling plots corresponding to (a) and (c), respectively, for data near the transition with $\xi =|g/g_c{-1|}^{-\nu }$ and the same parameters $g_c=1.426, z_0=2.3, z=1.2$, and $\nu =1.1$.

Figure 2

(a) Phase stiffness in the imaginary-time direction ${\gamma }_{\tau }$ for different system sizes $L$, near the transition point estimated from Fig. 1. $L_{\tau }=a{L}^z$, with aspect ratio $a=0.628$ and $z=1.25$. Inset: Scaling plot of ${\gamma }_{\tau }$ with $g_c=1.424$ and $\nu =0.97$. (b) Scaling plot of conductivity $\sigma \left(i{w}_n\right)$ at the critical coupling $g_c$ with $\alpha =0.15$. The universal conductivity is given by the intercept with the $x=0$ dashed line, leading to $\frac{{\sigma }^{*}}{{\sigma }_Q}=0.56\left(3\right)$. (c) Critical coupling $g_c$ at different values of the average frustration $f_o$ and increasing flux-disorder strength $D_f$. Inset: Behavior of the corresponding critical currents $I_c$ at $E_c=0$. (d) Resistivity ${\rho }^{*}=1/{\sigma }^{*}$ in units of ${\rho }_Q=1/{\sigma }_Q$ at the transition for the different average frustrations indicated in (c) and increasing flux disorder $D_f$.