Peter Armitage: Pedagogical review of AC response of really dirty superonductors

Here "really dirty" means that it is beyond conventional Mattis Bardeen
theory.

1. The talk start nevertheless with review of Mattis-Bardeen,
coherence factors, etc that can be found in Tinkham or anywhere else. What I (Ioffe)
did not know is that Habel-Slichter peak in σ1 only in 94. Optical sum rule.

2. Overview of InO physics for superconducting samples with relatively
high Tc>2K.

Sequence of the transitions (crossovers): normal state crosses over to a
state with large amplitude fluctuations but no long range order. Finally a
BKT transition to a true superconductor that occurs when TBKT=π/2 ρS (ρS is
superfluid stiffness).

Slowing down close to transition starting with the work of Tanner in 1974.

At finite frequency the BKT jump is smeared and BCS like ρS(T) reappears.

Scaling analysis of the conductivity gives characteristic frequency scaling
near Tc, which is roughly linear in (T-Tc)/ Tc .

3. Strongly disordered superconductors (InO).

Two scenarios:
A. Strong disorder might induce phase fluctuations without much
suppression of the amplitude.
B. Alternatively, the disorder might suppress the amplitude of the
order parameter first.

InO - high frequency measurements show perseverance of phase stiffness at
high frequencies even in the samples with a very high resistance. This is
direct evidence for scenario (A).

Appearance of non-zero conductivity at low frequencies may be evidence of
inhomogeneity, not of quasiparticles.

Blogged by Lev Ioffe