Critical fluctuations in $N$-component superconductor models

Klaus D. Usadel

R. F. Hassing

Alexei M. Tsvelik, Fabian H. L. Eßler

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.

Flavio S. Nogueira, Dirk Manske

The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type-II superconductors the dynamic critical exponent is given exactly by $z=3∕2$. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that $z=3∕2$ follows from the duality between the extreme type-II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations and at least one experiment.

Peter Mittelstaedt

Tingting Shi, Wei Zhang, C. A. R. Sá de Melo

Abstract We discuss standard and tighter upper bounds on the critical temperature T c of two-dimensional superfluids and superconductors versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen–Cooper–Schrieffer (BCS) to the Bose regime. We consider only one-band Hamiltonians, where the transition from the normal to the superfluid (superconducting) phase is governed by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and T c exists. The standard critical temperature upper bound T c up 1 is obtained from the Ferrell-Glover-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of the order parameter for superfluidity (superconductivity) and use the renormalization group to obtain the phase-fluctuation critical temperature T c θ , a much tighter bound to the critical temperature supremum than T c up 1 over a wide range of densities or filling factors. We also discuss a fundamental difference between superfluids and superconductors in regards to the vortex core energy dependence on density. Going beyond phase fluctuations, we note that theories including modulus fluctuations of the order parameter or particle-hole fluctuations valid throughout the BCS-Bose evolution are still lacking, but the inclusion of these fluctuations can only produce a critical temperature that is lower than T c θ and thus produce an even tighter bound to the critical temperature supremum. We conclude by indicating that if the measured critical temperature exceeds T c θ in experiments involving two-dimensional single-band systems, then a non-BKT mechanism must be invoked to describe the superfluid (superconducting) transition.