Contributor info: Prof. Mikhail Feigel'man

Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

SciPost Phys. 18, 010 (2025) · published 10 January 2025 | Toggle abstract · pdf

By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.

Igor Poboiko, Mikhail Feigel'man

SciPost Phys. 17, 066 (2024) · published 23 August 2024 | Toggle abstract · pdf

Recent experimental studies on strongly disordered indium oxide films have revealed an unusual first-order quantum phase transition between the superconducting and insulating states (SIT). This transition is characterized by a discontinuous jump from non-zero to zero values of superfluid stiffness at the critical point, contradicting the conventional "scaling scenario" typically associated with SIT. In this paper, we present a theoretical framework for understanding this first-order transition. Our approach is based on the concept of competition between two fundamentally distinct ground states that arise from electron pairs initially localized by strong disorder: the superconducting state and the Coulomb glass insulator. These ground states are distinguished by two crucially different order parameters, suggesting a natural expectation of a discontinuous transition between them at $T=0$. This transition occurs when the magnitudes of the superconducting gap $\Delta$ and the Coulomb gap $E_C$ become comparable. Additionally, we extend our analysis to low non-zero temperatures and provide a mean-field "phase diagram" in the plane of $(T/\Delta,E_C/\Delta)$. Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.

Dmitry E. Kiselov, Mikhail A. Skvortsov, Mikhail V. Feigel'man

SciPost Phys. 15, 008 (2023) · published 12 July 2023 | Toggle abstract · pdf

We calculate the quasiparticle density of states (DoS) inside the vortex core in a granular superconductor, generalizing the classical solution applicable for dirty superconductors. A discrete version of the Usadel equation for a vortex is derived and solved numerically for a broad range of parameters. Electron DoS is found to be gapful when the coherence length $\xi$ becomes comparable to the distance between neighboring grains $l$. Minigap magnitude $E_g$ grows from zero at $\xi \approx 1.4 l$ to third of superconducting gap $\Delta_0$ at $\xi \approx 0.5 l$. The absence of low-energy excitations is the main ingredient needed to understand strong suppression of microwave dissipation recently observed in a mixed state of granular Al.

B. V. Pashinsky, Mikhail V. Feigel'man, Anton V. Andreev

SciPost Phys. 14, 096 (2023) · published 4 May 2023 | Toggle abstract · pdf

Theory of linear microwave response of thin films of type-II superconductors in the mixed state is developed taking into account random spatial fluctuations of the parameters of the system, such as the order parameter, diffusion coefficient, or film thickness. In the regime of collective pinning the microwave response of the system exhibits strong frequency dispersion, arising from nonequilibrium vortex core quasiparticles. The corresponding contribution to the ac conductivity is controlled by the inelastic relaxation time, and may exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type inelastic relaxation. Debye mechanism of microwave losses may be responsible for strong effects of electromagnetic noise upon dc conductivity in the mixed state at low temperatures.

Khachatur G. Nazaryan, Mikhail Feigel'man

SciPost Phys. 14, 046 (2023) · published 23 March 2023 | Toggle abstract · pdf

We propose and study theoretically a new mechanism of electron-impurity scattering in doped seminconductors with large dielectric constant. It is based upon the idea of vector character of deformations caused in the crystalline lattice by any point defects siting asymmetrically in the unit cell. In result, local lattice compression due to the elastic deformations decay as $1/r^2$ with distance from impurity. Electron scattering (due to standard deformation potential) on such defects leads to low-temperature mobility $\mu(n)$ scaling with electron density $n$ of the form $\mu(n) \propto n^{-2/3}$ that is close to experimental observations on a number of relevant materials.

Aleksey. V. Lunkin, Mikhail . V. Feigel'man

SciPost Phys. 13, 073 (2022) · published 29 September 2022 | Toggle abstract · pdf

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal and temperature-dependent. At $\omega \gg T$ the conductivity $\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega \approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.

Aleksey V. Lunkin, Mikhail V. Feigel’man

SciPost Phys. 12, 031 (2022) · published 20 January 2022 | Toggle abstract · pdf

We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.