Discussion-session II report: Electrodynamics in strongly disordered superconductors

Suggested questions:

1. how and in what sense would one modify the standard Mattis-Bardeen treatment if applied to highly resistive superconductors.
2. how would one treat a possibly occurring nonlinear response (i.e. power dependence)

Additional questions raised:

· What are the sources of dissipation at frequencies much below the gap in highly disordered superconductors?

Status of the field:

1. Spectroscopy ongoing from 100 MHz to 20 GHz to determine the electronic properties of disordered materials, in particular InOx. All in the small signal limit and across the SIT.

2. User-driven experiments with superconducting resonators of TiN or NbTiN, with a preference for high resistivity but still about a factor of 10 off from the SIT. Signatures that standard Mattis-Bardeen works relatively well but deviations are being identified.

3. There is no specific theory yet for the electrodynamics of disordered superconductors, in view of the fact that the theory to understand the system as such is still under development.

Various remarks:

1. Roughly speaking one might characterize that superconducting state as consisting of percolating inductances, whereas the insulating state is more like percolating capacitors.

2. The non-linear regime is probably determined by Josephson weak links

3. Pump-probe experiments with microwaves might be illuminating to probe the nonlinear regime.

4. Nontrivial sources of dissipation may exist in superconductors with inhomogeneous superfluid density. In general, for resonator applications then, one wants to have highly resistive superconductors, which do not develop significant inhomogeneities.

Prepared by Teun Klapwijk and Peter Armitage