arXiv subjects

I. M. Khaymovich

Publications and source records attributed to I. M. Khaymovich.

At least 19 recordsLinked to original sources

arXiv2021

Electron-phonon heat transfer in giant vortex states

We examine energy relaxation of non-equilibrium quasiparticles in different vortex configurations in ``dirty'' $s$-wave superconductors. The heat flow from the electronic subsystem to phonons in a mesoscopic superconducting disk with a radius of the order of several coherence lengths is calculated both in the Meissner and giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap $E_{\rm g}$ is reduced by the Meissner currents. In order to uncover physical origin of the results, we develop a semiquantitative analytical approximation based on the combination of homogeneous solutions of Usadel equations in Meissner and vortex states of a mesoscopic superconducting disc and analytically calculate the corresponding spatially resolved electron-phonon heat rates. Our approach provides an important information about non-equilibrium quasiparticles cooling by the magnetic-field induced traps in various mesoscopic superconducting devices.

cond-mat.supr-con↗

arXiv2021

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

cond-mat.dis-nn↗

arXiv2021

Emergent fractal phase in energy stratified random models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

cond-mat.dis-nn↗

arXiv2021

Dynamical phases in a "multifractal" Rosenzweig-Porter model

We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the {\it averaged} survival probability may decay with time as the simple exponent, as the stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson model on Random Regular Graph (RRG) onto the "multifractal" RP model and find exact values of the stretch-exponent $κ$ depending on box-distributed disorder in the thermodynamic limit. As another example we consider the logarithmically-normal RP (LN-RP) random matrix ensemble and find analytically its phase diagram and the exponent $κ$. In addition, our theory allows to compute the shift of apparent phase transition lines at a finite system size and show that in the case of RP associated with RRG and LN-RP with the same symmetry of distribution function of hopping, a finite-size multifractal "phase" emerges near the tricritical point which is also the point of localization transition.

cond-mat.dis-nn↗

arXiv2020

Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model

In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a fragile weakly ergodic phase appears that is characterized by broken basis-rotation symmetry which the fully-ergodic phase, also present in this model, strictly respects in the thermodynamic limit. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model involves a jump in the fractal dimension of the eigenfunction support set. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.

cond-mat.dis-nn↗

arXiv2020

Renormalization to localization without a small parameter

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.

cond-mat.dis-nn↗

arXiv2020

Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble

Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase and ergodic transition have a status of a mathematical theorem. Yet, this phase in GRP model is oversimplified: the spectrum of fractal dimensions is degenerate and the mini-band in the local spectrum is not multifractal. In this paper we suggest an extension of the GRP model by adopting a logarithmically-normal (LN) distribution of off-diagonal matrix elements. A family of such LN-RP models is parametrized by a symmetry parameter $p$ and it interpolates between the GRP at $p\rightarrow 0$ and Levy ensembles at $p\rightarrow\infty$. A special point $p=1$ is shown to be the simplest approximation to the Anderson localization model on a random regular graph.We study in detail the phase diagram of LN-RP model and show that $p=1$ is a tricritical point where the multifractal phase first collapses. This collapse is shown to be unstable with respect to the truncation of the log-normal distribution. We suggest a new criteria of stability of the non-ergodic phases and prove that the Anderson transition in LN-RP model is discontinuous at all $p>0$.

cond-mat.dis-nn↗

arXiv2019

Robustness of delocalization to the inclusion of soft constraints in long-range random models

Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models is numerically observed and confirmed by the analytical calculations. First, matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum the inclusion of to soft constraints is generally discussed for single-particle and many-body systems.

cond-mat.dis-nn↗

arXiv2019

Higgs modes in proximized superconducting systems

The proximity effect in hybrid superconducting - normal metal structures is shown to affect strongly the coherent oscillations of the superconducting order parameter $Δ$ known as the Higgs modes. The standard Higgs mode at the frequency $2Δ$ is damped exponentially by the quasiparticle leakage from the primary superconductor. Two new Higgs modes with the frequencies depending on both the primary and induced gaps in the hybrid structure are shown to appear due to the coherent electron transfer between the superconductor and the normal metal. Altogether these three modes determine the long-time asymptotic behavior of the superconducting order parameter disturbed either by the electromagnetic pulse or the quench of the system parameters and, thus, are of crucial importance for the dynamical properties and restrictions on the operating frequencies for superconducting devices based on the proximity effect used, e.g., in quantum computing, in particular, with topological low-energy excitations.

cond-mat.supr-con↗

arXiv2019

Time-reversal symmetric Crooks and Gallavotti-Cohen fluctuation relations in driven classical Markovian systems

In this paper, we address an important question of the relationship between fluctuation theorems for the dissipated work $W_{d} = W-ΔF$ with general finite-time (like Jarzynski equality and Crooks relation) and infinite-time (like Gallavotti-Cohen theorem) drive protocols and their time-reversal symmetric versions. The relations between these kinds of fluctuation relations are uncovered based on the examples of a classical Markovian $N$-level system. Further consequences of these relations are discussed with respect to the possible experimental verifications.

cond-mat.stat-mech↗

arXiv2019

Correlation-induced localization

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.

cond-mat.dis-nn↗

arXiv2019

Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probability of finding the initial state after time $t$. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of $R(t)$ with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of $R(t\to\infty)=k$, finite in the thermodynamic limit $N\rightarrow\infty$, which approaches $k=R(t\to 0)$ in this limit.

cond-mat.dis-nn↗

arXiv2019

Electronic structure of mesoscopic superconducting disk: Quasiparticle tunneling between the giant vortex core and disk edge

The electronic structure of the giant vortex states in a mesoscopic superconducting disk is studied in a dirty limit using the Usadel approach. The local density of states profiles are shown to be strongly affected by the effect of quasiparticle (QP) tunneling between the states localized in the vortex core and the ones bound to the sample edge. Decreasing temperature leads to a crossover between the edge-dominated and core-dominated regimes in the magnetic field dependence of the tunneling conductance. This crossover is discussed in the context of the efficiency of quasiparticle cooling by the magnetic field induced QP traps in various mesoscopic superconducting devices.

cond-mat.supr-con↗

arXiv2018

Thermodynamics in Single-Electron Circuits and Superconducting Qubits

Classical and quantum electronic circuits provide ideal platforms to investigate stochastic thermodynamics and they have served as a stepping stone to realize Maxwell's demons with highly controllable protocols. In this article we first review the central thermal phenomena in quantum nanostructures. Thermometry and basic refrigeration methods will be described as enabling tools for thermodynamics experiments. Next we discuss the role of information in thermodynamics which leads to the concept of Maxwell's demon. Various Maxwell's demons realized in single-electron circuits over the past couple of years will be described. Currently true quantum thermodynamics in superconducting circuits is in focus of attention, and we end the review by discussing the ideas and first experiments in this exciting area of research.

cond-mat.stat-mech↗

arXiv2017

Nonlocality and dynamic response of Majorana states in fermionic superfluids

We suggest a microscopic model describing the nonlocal ac response of a pair of Majorana states in fermionic superfluids beyond the tunneling approximation. The time-dependent perturbations of quasiparticle transport are shown to excite finite period beating of the wavefunction between the distant Majorana states. We propose an experimental test to measure the characteristic time scales of quasiparticle transport through the pair of Majorana states defining, thus, quantitative characteristics of nonlocality known to be a generic feature of Majorana particles.

cond-mat.supr-con↗

arXiv2017

Distribution of current fluctuations in a bistable conductor

We measure the full distribution of current fluctuations in a single-electron transistor with a controllable bistability. The conductance switches randomly between two levels due to the tunneling of single electrons in a separate single-electron box. The electrical fluctuations are detected over a wide range of time scales and excellent agreement with theoretical predictions is found. For long integration times, the distribution of the time-averaged current obeys the large-deviation principle. We formulate and verify a fluctuation relation for the bistable region of the current distribution.

cond-mat.mes-hall↗

arXiv2016

Recovery of a SINIS turnstile accuracy in a strongly non-equilibrium regime

We perform a theoretical study of non-equilibrium effects in charge transport through a hybrid single-electron transistor based on a small normal metal (N) island with the gate-controlled number of electrons, tunnel-coupled to voltage-biased superconducting (S) electrodes (SINIS). Focusing on the turnstile mode of the transistor operation with the gate voltage driven periodically, and electrons on the island being out of equilibrium, we find that the current quantization accuracy is a non-monotonic function of the relaxation rate $Γ_{\mathcal{F}}$ of the distribution function $\mathcal{F}(ε)$ on the island due to tunneling, as compared to the drive frequency $f$, electron-electron $1/τ_{ee}$ and electron-phonon $1/τ_{eph}$ relaxation rates. Surprisingly, in the strongly non-equilibrium regime, $f\gg Γ_{\mathcal{F}}\ggτ_{ee}^{-1},τ_{eph}^{-1}$, the turnstile current plateau is recovered, similarly to the ideal equilibrium regime, $τ_{eph}^{-1}\gg Γ_{\mathcal{F}}$. The plateau is destroyed in the quasiequilibrium regime when the electron-electron relaxation is faster than tunneling.

cond-mat.mes-hall↗

arXiv2016

Quasiparticle trapping in Meissner and vortex states of mesoscopic superconductors

Nowadays superconductors serve in numerous applications, from high-field magnets to ultra-sensitive detectors of radiation. Mesoscopic superconducting devices, i.e. those with nanoscale dimensions, are in a special position as they are easily driven out of equilibrium under typical operating conditions. The out-of-equilibrium superconductors are characterized by non-equilibrium quasiparticles. These extra excitations can compromise the performance of mesoscopic devices by introducing, e.g., leakage currents or decreased coherence times in quantum devices. By applying an external magnetic field, one can conveniently suppress or redistribute the population of excess quasiparticles. In this article we present an experimental demonstration and a theoretical analysis of such effective control of quasiparticles, resulting in electron cooling both in the Meissner and vortex states of a mesoscopic superconductor. We introduce a theoretical model of quasiparticle dynamics which is in quantitative agreement with the experimental data.

cond-mat.mes-hall↗