Tuesday 28 July 2015- Peter Armitage- On the nature of below-gap dissipation in highly disordered superconductors

Peter Armitage introduces the general behavior of the optical conductivity of a superconductor. In particular the imaginary part of the conductivity is related to the Cooper pairs, which show up as a delta-peak in the real part of the conductivity. He points out that the size of this delta function is related to spectral weight that is “missing below the energy gap”.

This BCS-based Mattis-Bardeen prediction for the optical response is found in conventional superconductors (e.g. observed by Tinkham and coworkers a long time ago).

Peter suggests coupled 1D Josephson arrays as a “cartoon” model of springs, where an optically active mode shows up. If there is disorder involved, some spectral weight, which might be originally at zero frequency, then moves to finite frequency. Peter points out that he only wants to focus on below-gap features, but there might be effects above the gap as well. He then refers to the suggestion by Auerbach and coworkers that a Higgs mode might show up in the optical response of disordered superconductors, and he mentions that experiments in his own group, which correspond to those of the recent paper of Sherman et al., come to different experimental conclusions and that he believes that the Higgs mode does not apply here.

Peter then briefly introduces their own experiments: THz time domain spectroscopy. He shows a set of optical conductivity spectra for NbN thin films with different Tc. With suppressed Tc, the signature of the gap in the real part of the conductivity becomes more blurred, and the Cooper-pair response in the imaginary part becomes weaker. Peter then explains that fitting the data with a spread in gap values gives a reasonable description of the spectra in the real part of the conductivity. He refers to theoretical work by Larkin and Ovchinnikov: disorder on scales shorter than coherence length will give smeared BCS gap function.

Peter finally reports that for their optical measurements on disordered samples, the traditional sum rule is not obeyed when it comes to the delta-peak in the superconductor: apparently some spectral weight that is suppressed below the energy gap is shifted to higher energies instead of going into the delta-peak.

Blogged by Marc Scheffler