Tuesday 28 July 2015 - Misha Skvortsov - Density of states and Inhomogeneity in disordered superconductors

Misha starts with the general motivation: we have experimental (and theoretical) evidence than in disordered systems the local gap becomes inhomogeneous. How to describe this? Which are the consequences in the physical observables?

First of all, Misha clarifies the difference between “disorder” and “inhomogeneity”. When one talks about disorder one usually compares the superconducting correlation length xi with the mean-free path l, so that clean limit is for l/xi>>1, while dirty limit is the opposite. Inhomogeneity is something different, it has to do with the ratio between l and Fermi wavelength, and it implies the absence of self-averaging. Question by Dan Shahar: it can occur in principle also in a clean, correlated system. Answer by Misha: yes, but we try to make our life simpler first, and we stick on the case of disorder-induced inhomogeneity. In addition we want a small parameter to deal with, so we consider disordered systems but away from the SIT. Misha wants to focus on the effects of inhomogeneity on two measurable quantities: 1) the (tunneling) DOS and 2) the superfluid density.

For the DOS Misha first introduces the phenomenological Random-Coupling Constant (RCC) model by Larkin-Ovchinnikov: a space-dependent coupling constant can have the same effect as Abrikosov-Gorgov like magnetic impurities (as implemented by Usadel equations), i.e. smearing of the BCS coherence peak in the DOS plus a reduction of the hard gap. What’s new here is that the RCC model is derived starting from mesoscopic fluctuations of the order parameter. This allows one to connect the famous eta_DOS depairing parameter in Usadel equations to the SC order-parameter fluctuations. At the end one obtains both the smearing of the peaks and a tail below the hard gap. However, even using the kind of mesoscopic inhomogeneity that one expects in the model elaborated by Misha e coworkers for the Coulomb suppression of Tc, the overall effect on the DOS is 100 times smaller than the smearing observed in TiN films. Why? This remains an open interesting question (but see also comment at the end of the talk).

For what concerns the superfluid density Misha explains that an outcome of the RCC model is that the Cooperon and the diffuson get coupled in the presence of the gauge field. This implies that the superfluid density (i.e. the response to the gauge field) is not only suppressed by disorder in the usual Mattis-Bardeen sense (i.e. only a fraction of the total carries condense in the superfluid state) but it gets an additional suppression due to the mesoscopic order-parameter fluctuations. Once again, this can be mapped into the result of Usadel equations, BUT the depairing parameter eta_EM turns out to be different from the one eta_DOS that accounts for the DOS smearing: this is a quite relevant take-home message for experimentalist trying to fit data with the Usadel equations.

Finally, Misha makes an interesting comment on the fact that the different kinds of disorder (dense weak scatterers, or diluted strong scatterers, or grain boundaries, etc.) introduce different short-scale effects that can be finally relevant to explain the real mechanisms of Tc suppression and all the non-universal aspects of the experimental findings (including the quantitative discrepancies between theory and experiments). Indeed, even if on average only the diffusion coefficient matters, the mesoscopic fluctuations of the SC order parameters are very sensitive to short-scale structure of disorder. This question opens an interesting perspective for future theoretical and experimental work.

Blogged by Lara Benfatto