Quantum effects on renormalized superconducting fluctuations are studied in the context of vortex states. It is argued by taking account of existing resistivity data that inclusion of dissipative (metallic) dynamics is indispensable at any nonzero temperature. Analysis is largely based on simple extensions of the usual time-dependent Ginzburg–Landau (TDGL) dynamics to quantum regime. First, phase diagram and dc conductivities resulting from a quantum GL action with purely dissipative dynamics are investigated, and it is noticed that, on (or, in the vicinity of) the transition line between the vortex lattice and the resulting quantum vortex liquid regime, the inverse of vortex flow conductance becomes a nearly universal value of the order of R q = 6.45 ( k Ω) and independent of material parameters. On the other hands, based on the usual Feynman graph analysis of Kubo formula, the superconducing (i.e. fluctuation) contribution to dc diagonal conductance decreases upon cooling in the disordered phase affected by quantum fluctuations, and becomes zero in T = 0 liquid regime [and above Hc2 (0)] irrespective of the details of dynamics. Reflecting these theoretical results, calculated resistance curves show the behavior quite similar to those observed in homogeneously disordered thin films, even though the presence of a field-tuned insulator–superconductor transition at T = 0 is neglected and the dynamics is purely dissipative. Phenomena in systems with quantum fluctuation of moderate strength are also considered. Analysis is also extended to the cases with other dynamical terms. It is pointed out that the usual (mean field) vortex flow Hall conductivity is never found in any nondissipative T = 0 liquid regime, and argued that, in general, the superconducting Hall effect itself is absent there at low enough fields irrespective of the presence of particle–hole assymmetry. Therefore, in contrast to the thermal vortex states with no pinning disorder, the dc transport phenomena at T = 0 are quite sensitive to the corresponding phase diagram, and hence, discussions based on the single vortex dynamics are even qualitatively invalid in the liquid regime at extremely low temperatures.
Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph
