Frustration and disorder in granular superconductors

TLDR

The paper investigates ordered and disordered three‑dimensional arrays of weakly coupled superconducting grains embedded in a nonsuperconducting host subjected to a magnetic field. It aims to discuss how the predicted Tc(B) behavior affects kinetic inductance and other transport measurements. Monte Carlo and mean‑field studies show that ordered arrays exhibit a flux‑quantum periodic, anisotropic Tc(B) with complex substructure, while disordered arrays become gauge‑glass–like spin‑glasses at strong fields, with Tc dropping then saturating and, for weaker disorder, displaying damped oscillations, indicating that both ordered and disordered systems behave as anisotropic superfluids in a magnetic field.

Abstract

We consider the behavior of ordered and disordered three-dimensional weakly coupled arrays of superconducting grains embedded in a nonsuperconducting host and placed in a magnetic field $B$. In ordered simple-cubic arrays, with $\stackrel{\ensuremath{\rightarrow}}{B}$ parallel to a crystal axis and nearest-neighbor interactions, both Monte Carlo and molecular-field calculations show that ${T}_{c}$ is periodic in $B$ with a period of one flux quantum per unit square perpendicular to the field, and with complex substructure, as found previously in two-dimensional ordered arrays. The dependence of ${T}_{c}$ upon $\stackrel{\ensuremath{\rightarrow}}{B}$ is also shown to be highly anisotropic. Positionally disordered arrays are shown to behave at sufficiently strong fields very much like a spin-glass: They are, in fact, a physical realization of the "gauge glass" discussed by several authors. Varying the magnetic field, at strong fields, is equivalent to jumping from one "spin-glass replica" to another. Monte Carlo calculations for a model of dilute Pb spheres in a Zn host show a continuous transformation from an "$\mathrm{xy}$ ferromagnet" to spin-glass behavior: ${T}_{c}(B)$ first drops with increasing field, then saturates at strong fields. For weaker disorder, ${T}_{c}(B)$ is predicted to be a damped oscillating function of $B$. Both ordered and disordered samples are predicted to be anisotropic superfluids in a magnetic field. The implications of these predictions for measurements of kinetic inductance and other transport properties are briefly discussed.