Dynes superconductivity and the cuprates*

In a superconductor there exist two different types of scattering processes, depending on their action on the Cooper pairs: pair-conserving and pair-breaking. Making use of the microscopic coherent potential approximation, we have developed a phenomenological description of the so-called Dynes superconductors in which both processes are characterized by separate lifetimes [1]. Our theory solves the long-standing puzzle about the origin of the ubiquitous Dynes formula [2] for the tunneling density of states. It also predicts how the electron spectral functions change in presence of both types of scattering, correcting the previously used phenomenological two-lifetime expressions. In this talk, after introducing the concept of the Dynes superconductors, I will discuss its applicability to the d-wave cuprate superconductors, in which the two types of scattering processes correspond to small- and large-angle scattering. I will start by showing that, along fixed tomographic cuts, the Dynes phenomenology provides good fits of the electron spectral functions [3]. Then I will turn to a discussion of the recent electrodynamic experiments on overdoped cuprates [4,5]. I will show that the breakdown of the Homes law at extreme overdoping [4] is a generic property of the Dynes superconductors and I will discuss the relation between the dirty d-wave picture [6] and the Dynes phenomenology. The role of the Fermi liquid corrections and of the inelastic processes will also be discussed.

[1] F. Herman and R. Hlubina, Phys. Rev. B 94, 144508 (2016), Phys. Rev. B 95, 094514 (2017), Phys. Rev. B 96, 014509 (2017), Phys. Rev. B 97, 014517 (2018)
[2] R. C. Dynes et al., Phys. Rev. Lett. 41, 1509 (1978)
[3] T. Kondo et al., Nat. Commun. 6, 7699 (2015)
[4] I. Bozovic et al., Nature 536, 309 (2016)
[5] F. Mahmood et al., arXiv:1802.02101
[6] N. R. Lee-Hone et al., Phys. Rev. B 98, 054506 (2018)