Anton Khvalyuk

    ENS Lyon

    Low-Energy Theory of Strongly Disordered Superconductors

    Superconductivity is a thermodynamic state with zero electrical resistance below a material-dependent critical temperature, while also exhibiting expulsion of magnetic field and magnetic flux quantization in certain geometries [1]. These properties are described by the superfluid stiffness—a material-specific response constant, whose finite value is synonymous with superconductivity. In most superconductors, finite superfluid stiffness appears simultaneously with a hard gap in the excitation spectrum [1]. At low temperatures, this gap strongly suppresses thermal variations of physical quantities via the Boltzmann factor.
    Importantly for applications, superfluid stiffness manifests as kinetic inductance, distinct from the geometric inductance arising from magnetic fields surrounding any current-carrying conductor. Kinetic inductance is known to increase with the degree of microscopic nonmagnetic disorder: thin films of amorphous Indium Oxide exhibit kinetic inductance 500 times greater than the geometric inductance [4]. However, these films repeatedly contradict conventional theory: tunneling spectroscopy reveals a hard “pseudogap” above the critical temperature and strong emergent inhomogeneity of the superconducting state [2]. Moreover, superfluid stiffness exhibits a strong power-law temperature dependence (exponent ~1.6) at low temperatures, contradicting the gap-induced Boltzmann factor [3], while low-frequency dissipation decreases considerably with increasing temperature [4].
    In this talk, I will give a brief introduction to superconductivity, review the aforementioned experiments, and present a theoretical framework linking the measurements to material parameters, while also exposing the limits of existing models. This framework relates the key features of the macroscopic electromagnetic response to disorder‑induced spatial inhomogeneity of the superconducting state. I derive expressions for the superfluid stiffness and low‑frequency dissipation that match experimental data [3, 5]. The analysis identifies the low‑energy excitations causing the anomalous behavior as localized collective modes emerging from intrinsic inhomogeneity of the superconducting state, phenomenologically similar to two-level systems. These insights help explain the non‑monotonic shape of the superconducting transition line in the temperature–disorder plane [4].

    References:
    [1] M. Tinkham, Introduction to Superconductivity (Courier Corporation, 2004).
    [2] B. Sacépé et al., Nat. Phys 7, 239 (2011).
    [3] AVK et al., Phys. Rev. B 109, 144501 (2024).
    [4] Thibault Charpentier et al., Nat. Phys. 21, 104-109 (2025).
    [5] AVK and Mikhail V. Feigel’man, Phys. Rev. Lett. 136, 256001 (2026).