arXiv subjects

Mikhail Feigel'man

Publications and source records attributed to Mikhail Feigel'man.

17 recordsLinked to original sources

arXiv2026

Analytical Theory for Anomalous Diffusion in the Anderson Model with Heavy Tails

We develop an analytical theory of anomalous transport in a noninteracting Anderson model with heavy-tailed hopping amplitudes. The broad distribution of hopping amplitudes gives rise to an extended intermediate-time regime with a subdiffusive effective exponent, despite the absence of interactions or genuine many-body effects. By solving the transport equations analytically, we derive the time dependence of the mean-square displacement and identify a continuous crossover from an intermediate anomalous regime to asymptotically diffusive transport. As the localization transition is approached, the spatial extent of the subdiffusive window diverges parametrically, while the crossover to conventional diffusion remains finite in units of $\Gamma_0^{-1}$. This produces an increasingly broad anomalous transport regime in space that can closely resemble Griffiths-type transport observed near the many-body localization transition. Our results demonstrate that rare hopping processes alone provide a microscopic single-particle mechanism for robust transport anomalies, establishing an analytical benchmark for distinguishing interaction-induced effects from disorder-driven dynamics.

cond-mat.dis-nn↗

arXiv2026

Quantum critical collapse of a pinned vortex glass

The interplay between disorder and vortex--vortex interactions in strongly disordered superconductors in a magnetic field can stabilize a vortex-glass state, characterized by strong pinning and the absence of positional order. Yet its role in the destruction of superconductivity at the field-driven superconductor--insulator transition has remained unresolved. Here we use plasmonic microwave spectroscopy of superconducting resonators patterned from amorphous indium oxide thin films to directly track the superfluid density up to the critical field $B_c$. We find an unexpected resilience of the superfluid density, which decreases only logarithmically over nearly three orders of magnitude in field, in stark contrast to the rapid power-law suppression expected for vortex lattices. We attribute this anomalously slow decay to a collective vortex-pinning mechanism counterintuitively enhanced by vortex--vortex interactions. The superfluid density then vanishes linearly at $B_c$, where independent magnetoresistance measurements identify a continuous quantum critical point, unlike the abrupt transition observed at zero field. We further uncover an exceptionally large nonlinear electromagnetic response of the vortex glass, manifested as a pronounced positive-Kerr effect with potential for quantum sensing. These results show how disorder controls the critical magnetic field and identify the vortex glass as the key intermediate state governing the magnetic-field-induced superconductor--insulator transition.

cond-mat.supr-con↗

arXiv2025

Universal bound on microwave dissipation in superconducting circuits

Improving the coherence of superconducting qubits is essential for advancing quantum technologies. While superconductors are theoretically perfect conductors, they consistently exhibit residual energy dissipation when driven by microwave currents, limiting coherence times. Here, we report an empirical scaling relation between microwave dissipation and the superfluid density, a bulk property of superconductors related to charge carrier density and disorder. Our analysis spans a wide range of superconducting materials and device geometries, from highly disordered amorphous films to ultra-clean systems with record-high quality factors, including resonators, 3D cavities, and transmon qubits. This scaling reveals an intrinsic bulk dissipation channel, independent of surface dielectric losses, which we attribute to nonequilibrium quasiparticles trapped within disorder-induced spatial variations of the superconducting gap, with a density set by a universal material parameter. Our findings identify an empirical coherence limit associated with intrinsic material properties and provide a data-driven basis for materials selection in future superconducting quantum circuits.

cond-mat.mes-hall↗

arXiv2024

Mean-field theory of first-order quantum superconductor-insulator transition

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.

cond-mat.supr-con↗

arXiv2024

First-order quantum breakdown of superconductivity in amorphous superconductors

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait involves scaling laws governing a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here, we show a departure from this paradigm, showcasing that amorphous superconducting films of indium oxide undergo a distinctive, discontinuous first-order quantum phase transition tuned by disorder. Through systematic measurements of the plasmon spectrum in superconducting microwave resonators, we provide evidence for a marked jump of both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the previously overlooked role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, our investigation shows that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions into the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits.

cond-mat.mes-hall↗

arXiv2022

Low-temperature electron mobility in doped semiconductors with high dielectric constant

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 \textit{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.

cond-mat.mes-hall↗

arXiv2021

Theory of superconductivity due to Ngai's mechanism in lightly doped SrTiO3

We develop a theory of superconducting pairing in low-density Strontium titanate due to quadratic coupling of electron density to soft transverse optical phonons. It leads to static attractive potential between electrons which decay length scales inversely with soft optical gap. For low electron densities attraction between electrons is local and transition temperature Tc was found. The Tc(n) dependence in agreement with experimental data for low doping was calculated. Next, we show that suppression of Tc by hydrostatic pressure and strong increase of Tc due to isotop substitution are explained within our theory.

cond-mat.supr-con↗

arXiv2020

Quantum breakdown of superconductivity in low-dimensional materials

In order to understand the emergence of superconductivity it is useful to study and identify the various pathways leading to the destruction of superconductivity. One way is to use the increase in Coulomb-repulsion due to the increase in disorder, which overpowers the attractive interaction responsible for Cooper-pair formation. A second pathway, applicable to uniformly disordered materials, is the competition between superconductivity and Anderson localization, which leads to electronic granularity in which phase and amplitude fluctuations of the superconducting order parameter play a role. Finally, a third pathway is an array of superconducting islands coupled by some form of proximity-effect, due to Andreev-reflections, and which leads from a superconducting state to a state with finite resistivity, which appears like a metallic groundstate. This review summarizes recent progress in understanding of these different pathways, including experiments in low dimensional materials and application in superconducting quantum devices.

cond-mat.supr-con↗

arXiv2020

Two-dimensional Coulomb glass as a model for vortex pinning in superconducting films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase -- such as $\mathrm{In O}_x$, $\mathrm{Nb N}$, $\mathrm{Ti N}$, $\mathrm{Mo Ge}$, nano-granular aluminium, and others -- is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with large kinetic inductance per square $L_K$. Distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap, i.e. the probability to find a weakly pinned vortex is extremely low.

cond-mat.dis-nn↗

arXiv2020

Strange metal state near quantum superconductor-metal transition in thin films

We develop a theory of quantum $T = 0$ phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations $δλ(r)$ of the Cooper attraction constant. When strength of fluctuations $δλ(r)$ exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant $λ$. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance $\propto 1/r^β$ , with $2 < β\le 3$. We account for this interaction by means of a real-space strong-disorder renormalization group (RG). Near the q-SMT the RG flow is, formally, a dual equivalent of the Kosterlitz-Thouless RG. The corresponding line of fixed points describes a Griffiths phase of a metal with large fractal clusters of superconducting islands. Typical number of islands in a cluster grows as $N_δ\sim 1/δ$, where $0 < δ\ll 1 $ is the distance to the critical point. Superconducting side is described by a runaway of RG trajectories into the strong-coupling region. Close to the transition point on the SC side, $0<-δ\ll 1$, RG trajectories possess an extremum as function of the RG parameter $|δ|^{1/2} \ln(1/Tτ)$. It results in a wide temperature range where physical properties are nearly $T$-independent. This observation may be relevant to the understanding of a \emph{strange metal} state frequently observed near q-SMT.

cond-mat.supr-con↗

arXiv2019

Non-ergodic extended phase of the Quantum Random Energy model

The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized states is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin-spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a 'hyperglass' in which dynamics is practically absent. We discuss the implications of these finding to quantum information problems.

cond-mat.dis-nn↗

arXiv2017

Paraconductivity of pseudogapped superconductors

We calculate Aslamazov-Larkin paraconductity $σ_{AL}(T)$ for a model of strongly disordered superconductors (dimensions $d=2,3$) with a large pseudogap whose magnitude strongly exceeds transition temperature $T_c$. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same $ε= (T-T_c)/T_c$. Upon decreasing $ε$, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at $ε\leq ε_1 \ll 1 $. Characteristic scale $ε_1 $ is much larger than the width $ε_2$ of the thermodynamical critical region, that is determined via the Ginzburg criterion, $ε_2 \approx ε_1^d$. We argue that in the intermediate region $ε_2 \leq ε\leq ε_1$ paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at $ε\leq ε_2$; in particular, conductivity occurs to be strongly inhomogeneous in real space.

cond-mat.supr-con↗

arXiv2016

Spin correlation functions and quasiparticle decay

We study one-dimensional anisotropic XXZ spin-$\frac12$ model with ferromagnetic sign of the coupling and $z-z$ exchange constant $J_z = ΔJ$, where $Δ< 1$, and $J$ is the coupling within XY spin plane. We calculate damping of low-energy excitations with $ω\ll T $ due to their scattering from thermal excitation bath with temperature $T \ll J$, taking into account nonzero curvature of the excitation spectrum, $ε(q) = u q + δε(q)$. We calculate also longitudinal spin-spin correlation function $\langle S^z(x,t)S^z(0,0) \rangle$ at $x \approx ut$ and find the shape of the spreading "wave packet".

cond-mat.str-el↗

arXiv2015

Thermal transport in disordered one-dimensional spin chains

We study one-dimensional anisotropic XY-Heisenberg spin-$\frac{1}{2}$ chain with weak random fields $h_i^z S^z_i$ by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First we investigate phase diagram of the system in terms of dimensionless disorder $γ= \left /J^2 \ll 1$ and anisotropy parameter $Δ= J_z/J_{xy}$ and find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws. Then we use the diagram technique in terms of plasmon excitations to study low-temperature behavior of heat conductivity $κ$ and spin conductivity $σ$ in this power-law phase. The obtained Lorentz number $L \equiv κ/σT$ differs from the value derived earlier by means of memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.

cond-mat.mes-hall↗

arXiv2012

Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels which aquire a finite width. The important question is what is the driving force and the mechanism of transition(s) between two different types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy level statistics of a system of spins-1/2 with anisotropic exchange interactions and random transverse fields. Our results present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in a class of random spin models. Because this model also describes the physics of the superconductor-insulator transition in disordered superconductors like InO and similar materials, our results imply the appearance of novel insulating phases in the vicinity of this transition.

cond-mat.mes-hall↗

arXiv1996

Electrostatics of Vortices in Type II Superconductors

In a type II superconductor the gap variation in the core of a vortex line induces a local charge modulation. Accounting for metallic screening, we determine the line charge of individual vortices and calculate the electric field distribution in the half space above a field penetrated superconductor. The resulting field is that of an atomic size dipole ${\bf d} \sim e a_{\rm B} {\bf {\hat z}}$, $a_{\rm B} = \hbar^2/m e^2$ is the Bohr radius, acting on a force microscope in the pico to femto Newton range.

cond-mat↗

arXiv1995

Vortex Dynamics and the Hall-Anomaly: a Microscopic Analysis

We present a microscopic derivation of the equation of motion for a vortex in a superconductor. A coherent view on vortex dynamics is obtained, in which {\it both} hydrodynamics {\it and} the vortex core contribute to the forces acting on a vortex. The competition between these two provides an interpretation of the observed sign change in the Hall angle in superconductors with mean free path $l$ of the order of the coherence length $ξ$ in terms of broken particle-hole symmetry, which is related to details of the microscopic mechanism of superconductivity.

supr-con↗