Dynamics of granular superconductors at zero and large magnetic fields: Glassy behavior.

Abstract

We calculate the transport properties of a model granular superconductor in zero magnetic field and in a strong random magnetic field. The Hamiltonian is taken as the sum of two terms: a Josephson interaction coupling neighboring phases and a diagonal charging energy. The noncommutativity of charge and phase is neglected (classical, or large-grain, limit), as is dissipation occurring through shunt resistances connecting neighboring grains. The dynamical properties, including current-current correlation functions, conductivities, and voltage noise, are calculated as a function of temperature via molecular-dynamics techniques. For a simple-cubic lattice in zero magnetic field, the model exhibits the expected insulator-to-superconductor transition near ${\mathit{T}}_{\mathit{c}}$=2.2${\mathit{E}}_{\mathit{J}}$/${\mathit{k}}_{\mathit{B}}$, where ${\mathit{E}}_{\mathit{J}}$ is the Josephson coupling energy. The frequency-dependent conductivity has a strong fluctuation peak near ${\mathit{T}}_{\mathit{c}}$. Its behavior above ${\mathit{T}}_{\mathit{c}}$ is qualitatively reproduced by a simple Aslamasov-Larkin-like model. The voltage noise has a time correlation function, which oscillates below ${\mathit{T}}_{\mathit{c}}$ but falls off nearly monotonically above ${\mathit{T}}_{\mathit{c}}$. Its low-temperature behavior is explained analytically in terms of a model of voltage fluctuations due to propagating phase waves. A disordered system in a strong magnetic field is modeled by grains on a simple-cubic lattice with random magnetic phase factors on each bond, following Huse and Seung. Evidence for a vortex-fluid-to-vortex-glass transition is found from the increasingly slow decay of the current-current correlation function above ${\mathit{T}}_{\mathit{g}}$\ensuremath{\approxeq}0.45${\mathit{E}}_{\mathit{J}}$/${\mathit{k}}_{\mathit{B}}$, and from its nonergodic behavior below ${\mathit{T}}_{\mathit{g}}$. The behavior is similar to that found by Leutheusser from an analytic model of a structural liquid-glass transition.