Quantum Fluctuations of the Order Parameter in Superconductors

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This award supports theoretical research and education to study quantum fluctuations in low-dimensional superconductors. Three projects are planned: (1) The investigators will calculate corrections to the existing mean-field theory of the upper critical field in thin superconducting films. They will consider mesoscopic effects in the distribution of impurities that lead to the appearance of superconducting droplets above the BCS upper critical field. The Josephson network of the superconducting droplets may become macroscopically superconducting at low temperatures. The genuine transition point is determined by the interplay of the quantum fluctuations of the order parameter and the proximity effect. The behavior of various physical quantities near the transition will be considered and contact with the existing scaling theory will be made. (2) The investigators will construct a theory of the zero-temperature superconducting transition in finite-length wires and chains of Josephson junctions. This work is motivated by experiments that show deviations from a thermally activated resistivity at low temperatures. (3) The investigators will calculate I-V characteristics for a ferromagnet - d-wave superconductor junction including the effects of spin-orbit coupling. Diagrammatic expansions and the Keldysh technique are among the variety of analytical techniques that will be used. %%% This award supports theoretical research and education on quantum mechanical fluctuations in superconductors at low temperatures. The investigators will use advanced theoretical methods to study the role of quantum fluctuations in thin superconducting films, superconducting wires, and junctions involving superconductors. This research is fundamental and has potential impact on our understanding of quantum phase transitions in other systems.***