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Springer eBooks, 2018
We use quasiclassical methods of superconductivity to study the superconducting proximity effect ... more We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological p-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed nonlinear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire corresponding to time. This mapping allows to obtain exact solutions in the disordered nanowire in terms of elliptic functions. A surprising result that comes out of this solution is that the p-wave superconductivity proximity-induced into the disordered metal remains long-range, decaying as slowly as the conventional s-wave superconductivity. It is also shown that impurity scattering leads to the appearance of a zero-energy peak.
Physical review, Aug 11, 2016
We investigate dynamical many-body localization and delocalization in an integrable system of per... more We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.
Bulletin of the American Physical Society, Mar 13, 2017
Bulletin of the American Physical Society, Mar 6, 2014
Physical Review Special Topics - Accelerators and Beams, 2013
Physical Review Research
The hydrodynamic behavior of electron fluids in a certain range of temperatures and densities is ... more The hydrodynamic behavior of electron fluids in a certain range of temperatures and densities is well established in graphene and in two-dimensional semiconductor heterostructures. The hydrodynamic regime is intrinsically based on electron-electron interactions, and therefore it provides a unique opportunity to study electron correlations. Unfortunately, in simple longitudinal resistance measurements, the relative contribution of hydrodynamic effects to transport is rather small, especially at higher temperatures. Viscous hydrodynamic effects are masked by impurities, interaction with phonons, uncontrolled boundaries, and ballistic effects. This essentially limits the accuracy of measurements of electron viscosity. Fundamentally, what causes viscous friction in the electron fluid is the property of the flow called vorticity. In this paper, we propose to use micromagnets to increase the vorticity by orders of magnitude. Experimental realization of this proposal will bring electron hydrodynamics to a qualitatively new precision level, as well as opening a new way to characterize and externally control the electron fluid.
Gravitational Theories Beyond General Relativity, 2018
We investigate dynamical many-body localization and delocalization in an integrable system of per... more We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.
Gravitational Theories Beyond General Relativity, 2018
We consider three quantum many-body systems motivated by recent developments in condensed matter ... more We consider three quantum many-body systems motivated by recent developments in condensed matter physics, namely topological superconductivity, strongly interacting Bose-Einstein condensates and many-body localization with periodically driven systems. In each of the three problems, an analogy with classical mechanics is employed in the solution of the problem and the interpretation of results. These analogies, in addition to facilitating the solution, illustrate how unique features of classical mechanics or macroscopic phenomena such as macroscopic order parameter and observables, hydrodynamics, spacetime curvature, noise and dissipation, chaos and delocalization emerge out of quantum mechanics. The three problems we study
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing ... more Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons that occur only in very strong fields found in neutron stars or heavy ion colliders. We show that strong nonlinearity arises in Dirac materials at much lower fields ∼ 1T, allowing us to explore the extremely high field limit of quantum electrodynamics in solids. We explain recent experiments in a unified framework and predict nonlinear magneto-electric response, including a magnetic enhancement of dielectric constant and electrically induced magnetization. We propose experiments and discuss the applications on novel materials.
We review theoretical and experimental highlights in transport in two-dimensional materials focus... more We review theoretical and experimental highlights in transport in two-dimensional materials focussing on key developments over the last five years. Topological insulators are finding applications in magnetic devices, while Hall transport in doped samples and the general issue of topological protection remain controversial. In transition metal dichalcogenides valley-dependent electrical and optical phenomena continue to stimulate state-of-the-art experiments. In Weyl semimetals the properties of Fermi arcs are being actively investigated. A new field, expected to grow in the near future, focuses on the non-linear electrical and optical responses of topological materials, where fundamental questions are once more being asked about the intertwining roles of the Berry curvature and disorder scattering. In topological superconductors the quest for chiral superconductivity, Majorana fermions and topological quantum computing is continuing apace.
Physical Review Letters
The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we sh... more The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we show that statistical correlations between the charge-spin disorder sectors strongly affect the conductivity and the sign/magnitude of AHE. As the correlation between the charge and gauge-mass components increases, so does the AHE, achieving its universal value, and even exceed it, although the system is an impure metal.The AHE can change sign when the anti-correlations reverse the sign of the effective Dirac mass, a possible mechanism behind the sign change seen in recent experiments.
It is widely accepted that one of the reasons for appearance of the RF breakdown which limits ope... more It is widely accepted that one of the reasons for appearance of the RF breakdown which limits operation of high-gradient accelerating structures is the electron dark current [1]. This field emitted current, usually considered as a precursor of the breakdown, can be emitted from apexes of micro-protrusions on a structure surface. Therefore field and thermal processes in such protrusions deserve careful studies [2, 3]. The goal of our first study [3] was to analyze 2D process of RF field penetration inside protrusion of a metal with finite conductivity and to study corresponding Joule heating. In the current study, it is found that space charges can have a stabilizing effect on the electric field. We include a modification of the 1D model described in [4]. Moreover, we include into consideration, first, the Nottingham effect which may significantly change the protrusion heating. We also investigate the interplay between high temperature gradients and electric fields (Thomson heating)....
Physical Review B, 2015
We use quasiclassical methods of superconductivity to study the superconducting proximity effect ... more We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological p-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed nonlinear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire corresponding to time. This mapping allows to obtain exact solutions in the disordered nanowire in terms of elliptic functions. A surprising result that comes out of this solution is that the p-wave superconductivity proximity-induced into the disordered metal remains long-range, decaying as slowly as the conventional s-wave superconductivity. It is also shown that impurity scattering leads to the appearance of a zero-energy peak. arXiv:1408.4395v1 [cond-mat.supr-con]
Springer eBooks, 2018
We use quasiclassical methods of superconductivity to study the superconducting proximity effect ... more We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological p-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed nonlinear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire corresponding to time. This mapping allows to obtain exact solutions in the disordered nanowire in terms of elliptic functions. A surprising result that comes out of this solution is that the p-wave superconductivity proximity-induced into the disordered metal remains long-range, decaying as slowly as the conventional s-wave superconductivity. It is also shown that impurity scattering leads to the appearance of a zero-energy peak.
Physical review, Aug 11, 2016
We investigate dynamical many-body localization and delocalization in an integrable system of per... more We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.
Bulletin of the American Physical Society, Mar 13, 2017
Bulletin of the American Physical Society, Mar 6, 2014
Physical Review Special Topics - Accelerators and Beams, 2013
Physical Review Research
The hydrodynamic behavior of electron fluids in a certain range of temperatures and densities is ... more The hydrodynamic behavior of electron fluids in a certain range of temperatures and densities is well established in graphene and in two-dimensional semiconductor heterostructures. The hydrodynamic regime is intrinsically based on electron-electron interactions, and therefore it provides a unique opportunity to study electron correlations. Unfortunately, in simple longitudinal resistance measurements, the relative contribution of hydrodynamic effects to transport is rather small, especially at higher temperatures. Viscous hydrodynamic effects are masked by impurities, interaction with phonons, uncontrolled boundaries, and ballistic effects. This essentially limits the accuracy of measurements of electron viscosity. Fundamentally, what causes viscous friction in the electron fluid is the property of the flow called vorticity. In this paper, we propose to use micromagnets to increase the vorticity by orders of magnitude. Experimental realization of this proposal will bring electron hydrodynamics to a qualitatively new precision level, as well as opening a new way to characterize and externally control the electron fluid.
Gravitational Theories Beyond General Relativity, 2018
We investigate dynamical many-body localization and delocalization in an integrable system of per... more We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.
Gravitational Theories Beyond General Relativity, 2018
We consider three quantum many-body systems motivated by recent developments in condensed matter ... more We consider three quantum many-body systems motivated by recent developments in condensed matter physics, namely topological superconductivity, strongly interacting Bose-Einstein condensates and many-body localization with periodically driven systems. In each of the three problems, an analogy with classical mechanics is employed in the solution of the problem and the interpretation of results. These analogies, in addition to facilitating the solution, illustrate how unique features of classical mechanics or macroscopic phenomena such as macroscopic order parameter and observables, hydrodynamics, spacetime curvature, noise and dissipation, chaos and delocalization emerge out of quantum mechanics. The three problems we study
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing ... more Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons that occur only in very strong fields found in neutron stars or heavy ion colliders. We show that strong nonlinearity arises in Dirac materials at much lower fields ∼ 1T, allowing us to explore the extremely high field limit of quantum electrodynamics in solids. We explain recent experiments in a unified framework and predict nonlinear magneto-electric response, including a magnetic enhancement of dielectric constant and electrically induced magnetization. We propose experiments and discuss the applications on novel materials.
We review theoretical and experimental highlights in transport in two-dimensional materials focus... more We review theoretical and experimental highlights in transport in two-dimensional materials focussing on key developments over the last five years. Topological insulators are finding applications in magnetic devices, while Hall transport in doped samples and the general issue of topological protection remain controversial. In transition metal dichalcogenides valley-dependent electrical and optical phenomena continue to stimulate state-of-the-art experiments. In Weyl semimetals the properties of Fermi arcs are being actively investigated. A new field, expected to grow in the near future, focuses on the non-linear electrical and optical responses of topological materials, where fundamental questions are once more being asked about the intertwining roles of the Berry curvature and disorder scattering. In topological superconductors the quest for chiral superconductivity, Majorana fermions and topological quantum computing is continuing apace.
Physical Review Letters
The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we sh... more The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we show that statistical correlations between the charge-spin disorder sectors strongly affect the conductivity and the sign/magnitude of AHE. As the correlation between the charge and gauge-mass components increases, so does the AHE, achieving its universal value, and even exceed it, although the system is an impure metal.The AHE can change sign when the anti-correlations reverse the sign of the effective Dirac mass, a possible mechanism behind the sign change seen in recent experiments.
It is widely accepted that one of the reasons for appearance of the RF breakdown which limits ope... more It is widely accepted that one of the reasons for appearance of the RF breakdown which limits operation of high-gradient accelerating structures is the electron dark current [1]. This field emitted current, usually considered as a precursor of the breakdown, can be emitted from apexes of micro-protrusions on a structure surface. Therefore field and thermal processes in such protrusions deserve careful studies [2, 3]. The goal of our first study [3] was to analyze 2D process of RF field penetration inside protrusion of a metal with finite conductivity and to study corresponding Joule heating. In the current study, it is found that space charges can have a stabilizing effect on the electric field. We include a modification of the 1D model described in [4]. Moreover, we include into consideration, first, the Nottingham effect which may significantly change the protrusion heating. We also investigate the interplay between high temperature gradients and electric fields (Thomson heating)....
Physical Review B, 2015
We use quasiclassical methods of superconductivity to study the superconducting proximity effect ... more We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological p-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed nonlinear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire corresponding to time. This mapping allows to obtain exact solutions in the disordered nanowire in terms of elliptic functions. A surprising result that comes out of this solution is that the p-wave superconductivity proximity-induced into the disordered metal remains long-range, decaying as slowly as the conventional s-wave superconductivity. It is also shown that impurity scattering leads to the appearance of a zero-energy peak. arXiv:1408.4395v1 [cond-mat.supr-con]