Anton Khvalyuk : Low-energy theory of strongly disordered superconductors

Macroscopic electromagnetic response of a superconductor is described by a finite superfluid stiffness, which underlies hallmark phenomena such as dissipationless current flow and the Meissner effect. In conventional superconductors a hard excitation gap allows these properties to persist at finite temperature and frequency, enabling advanced superconducting technologies. The standard Mattis Bardeen framework further predicts that increasing disorder reduces the superfluid stiffness, thereby raising the kinetic inductance—a desirable trait for microwave device applications.
However, heavily disordered samples deviate from the conventional BCS-like theory in numerous ways. For example, both the phase diagram and tunneling spectroscopy reveal a hard “pseudogap” persisting above the transition temperature and unusually large sub gap dissipation. Furthermore, the suppression of the superfluid stiffness with temperature follows an unexpected power law spanning more than a decade of temperature [1], and the microwave dissipation shows a non monotonic temperature trend that cannot be explained by conventional means [2, 3].
I will briefly review the aforementioned experiments and present a theoretical framework that connects these measurements to intrinsic material parameters, while also exposing the limits of existing models. A combination of numerical simulations and theoretical analysis links the key features of the macroscopic electromagnetic response to disorder induced spatial inhomogeneity of the superconducting state. By analytically characterizing the associated statistical distribution, I derive expressions for both the superfluid stiffness and low frequency dissipation that agree with experimental data [1, 3].
The analysis identifies the low energy excitations responsible for the anomalous behavior as localized collective modes emerging from intrinsic inhomogeneity of the superconducting state that appear phenomenologically similar to two-level systems. These insights help explain the non monotonic shape of the superconducting transition line in the temperature–disorder plane [2].

[1] AVK, Thibault Charpentier, Nicolas Roch, Benjamin Sacépé, Mikhail V. Feigel’man,
Phys. Rev. B 109, 144501 (2024)
[2] Thibault Charpentier et al, Nature Physics 21, 104-109 (2025)
[3] AVK and Mikhail V. Feigel’man, arXiv:2512.11636