Kinetic inductance of Josephson-junction arrays: Dynamic and equilibrium calculations
Wenbin Yu, D. Stroud
DOI 10.1103/PhysRevB.50.13632 · Physical Review B
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Abstract
The low-frequency inverse kinetic inductance L−1 of an overdamped junction array at temperature T=0 is shown to equal that of an equivalent impedance network. The ijth bond of the network has an inverse inductance (2eEij/ħ)cos(θi0-θj0-Aij), where Eij is the Josephson coupling energy of the ijth bond, θi0 is the ground-state phase of the grain i, and Aij is the usual magnetic phase factor. Using this theorem, we calculate L−1 for square lattices as large as 180×180. The calculated L−1 agrees well with the T=0 limit of the helicity modulus γ calculated by conventional Monte Carlo techniques. In triangular arrays, the Monte Carlo calculation of γ yields a series of peaks at frustrations f=1/2(1-1/N), where N is an integer ≥2, consistent with experiments.
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