Universal criterion for the onset of superconductivity in granular films
Richard A. Ferrell, Behzad Mirhashem
DOI 10.1103/PhysRevB.37.648 · Physical Review B
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Abstract
In a granular film, modeled by a Josephson-coupled lattice, virtual tunneling of quasiparticles results in a critical value R□c for the normal-state sheet resistance. R□c is a universal upper bound for zero-temperature superconductivity and is computed in descending powers of z, the number of grain neighbors. Mean-field theory for a square lattice gives the leading term R□c=5.7 kΩ. For the fractional correction from the next term in the expansion, the Bethe approximation gives −35Z2, or -4% for Z=4.
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