arXiv subjects

Victor Galitski

Publications and source records attributed to Victor Galitski.

At least 91 records · Page 5Linked to original sources

arXiv2017

Enriched axial anomaly in Weyl materials

While quantum anomalies are often associated with the breaking of a classical symmetry in the quantum theory, their anomalous contributions to observables remain distinct and well-defined even when the symmetry is broken from the outset. This paper explores such anomalous contributions to the current, originating from the axial anomaly in a Weyl semimetal, and in the presence of a generic Weyl node-mixing term. We find that apart from the familiar anomalous divergence of the axial current proportional to a product of electric and magnetic fields, there is another anomalous term proportional to a product of the electric field and the orientation of a spin-dependent node-mixing vector. We obtain this result both by a quantum field-theoretic analysis of an effective Weyl action and solving an explicit lattice model. The extended spin-mixing mass terms, and the enriched axial anomaly they entail, could arise as mean-field or proximity-induced order parameters in spin-density-wave phases in Weyl semimetals or be generated dynamically within a Floquet theory.

cond-mat.mes-hall↗

arXiv2017

Dynamical Localization of Coupled Relativistic Kicked Rotors

A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016)], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.

cond-mat.dis-nn↗

arXiv2017

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, $\hbar \to 0$, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator, $C(t)$, for the classical and quantum kicked rotor -- a textbook driven chaotic system -- and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength $K$, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as $K \to 0$, while the OTOC's growth rate may decrease much slower showing higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time $t_E$: transitioning from a time-independent value of $t^{-1} \ln{C(t)}$ at $t < t_E$ to its monotonous decrease with time at $t>t_E$. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996); Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.

cond-mat.dis-nn↗

arXiv2016

Amperean Pairing at the Surface of Topological Insulators

The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards a superconducting state with unusual pairing, dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a ferromagnetic layer deposited on the surface of a topological insulator couple to the electrons as gauge fields. The transverse components of the magnetic gauge fields are unscreened and can mediate an effective interaction between electrons. There is an attractive interaction between electrons with momenta in the same direction which makes the pairing to be of Amperean type. We show that this attractive interaction leads to a $p$-wave pairing instability of the Fermi surface in the Cooper channel.

cond-mat.str-el↗

arXiv2016

Dynamical many-body localization in an integrable model

We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The Hamiltonian we investigate is linear in momentum, and its Floquet evolution operator is analytically tractable for arbitrary interaction strengths. One of the hallmarks of this model is that depending on certain parameters, it manifest both localization and delocalization in momentum space. We explicitly show that for this model, the energy being bounded at long times is not a sufficient condition for dynamical localization. Besides integrals of motion associated to the integrability, this model manifests additional integrals of motion, which are the exclusive consequence of dynamical many-body localization. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.

cond-mat.dis-nn↗

arXiv2016

Parity effect in a mesoscopic Fermi gas

We develop a quantitative analytic theory that accurately describes the odd-even effect observed experimentally in a one-dimensional, trapped Fermi gas with a small number of particles [G. Zürn et al., Phys. Rev. Lett. 111, 175302 (2013)]. We find that the underlying physics is similar to the parity effect known to exist in ultrasmall mesoscopic superconducting grains and atomic nuclei. However, in contrast to superconducting nanograins, the density (Hartree) correction dominates over the superconducting pairing fluctuations and leads to a much more pronounced odd-even effect in the mesoscopic, trapped Fermi gas. We calculate the corresponding parity parameter and separation energy using both perturbation theory and a path integral framework in the mesoscopic limit, generalized to account for the effects of the trap, pairing fluctuations, and Hartree corrections. Our results are in an excellent quantitative agreement with experimental data and exact diagonalization. Finally, we discuss a few-to-many particle crossover between the perturbative mesoscopic regime and non-perturbative many-body physics that the system approaches in the thermodynamic limit.

cond-mat.quant-gas↗

arXiv2016

Non-Markovian quantum friction of bright solitons in superfluids

We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from the first principle. The equation contains a stochastic Langevin force (associated with quantum noise) and a non-local in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton/particle interacts with excitations/radiation originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.

cond-mat.quant-gas↗

arXiv2016

Transport of Dirac electrons in a random magnetic field in topological heterostructures

We consider the proximity effect between Dirac states at the surface of a topological insulator and a ferromagnet with easy plane anisotropy, which is described by the \emph{XY}-model and undergoes a Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The surface states of the topological insulator interacting with classical magnetic fluctuations of the ferromagnet can be mapped onto the problem of Dirac fermions in a random magnetic field. However, this analogy is only partial in the presence of electron-hole asymmetry or warping of the Dirac dispersion, which results in screening of magnetic fluctuations. Scattering at magnetic fluctuations influences the behavior of the surface resistivity as a function of temperature. Near the BKT phase transition temperature we find that the resistivity of surface states scales linearly with temperature and has a clear maximum which becomes more pronounced as the Fermi energy decreases. Additionally at low temperatures we find linear resistivity, usually associated with non-Fermi liquid behavior, however here it appears entirely within the Fermi liquid picture.

cond-mat.mes-hall↗

arXiv2016

Anomalous Coulomb Drag in Electron-Hole Bilayers due to the Formation of Excitons

Several recent experiments have reported an anomalous temperature dependence of the Coulomb drag effect in electron-hole bilayers. Motivated by these puzzling data, we study theoretically a low-density electron-hole bilayer, where electrons and holes avoid quantum degeneracy by forming excitonic molecules. We describe the ionization-recombination crossover between the electron-hole plasma and exciton gas and calculate both the intralayer and drag resistivity as a function of temperature. The latter exhibits a minimum followed by a sharp upturn at low temperatures in a qualitative agreement with the experimental observations [see, e.g., J. A. Seamons et al., Phys. Rev. Lett. 102, 026804 (2009)]. Importantly, the drag resistivity in the proposed scenario is found to be rather insensitive to a mismatch in electron and hole concentrations in sharp contrast to the scenario of electron-hole Cooper pairing.

cond-mat.mes-hall↗

arXiv2015

Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators

We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac nodes on the surface, but only two of them are energetically degenerate and exhibit an energy offset relative to the third one. With a tunable chemical potential, when the surface states host electron and hole pockets of comparable size, strong interactions may drive this system into rotational symmetry breaking nematic and translational symmetric breaking excitonic spin- or charge-density-wave phases, depending on the relative chirality of the Dirac cones. Taking a realistic surface band structure into account we analyze the associated Ginzburg-Landau theory and compute the mean field phase diagram for interacting surface states. Beyond mean field theory, this system can be described by a two-component isotropic Ashkin-Teller model at finite temperature, and we outline the phase diagram of this model. Our theory provides a possible explanation of recent measurements which detect a two-fold symmetric magnetoresistance and an upturn in surface resistivity with tunable gate voltage in SmB$_6$. Our discussion can also be germane to other cubic topological insulators, such as ytterbium hexaboride (YbB$_6$), plutonium hexaboride (PuB$_6$).

cond-mat.mes-hall↗

arXiv2015

Gigantic surface life-time of an intrinsic topological insulator revealed via time-resolved (pump-probe) ARPES

The interaction between light and novel two-dimensional electronic states holds promise to realize new fundamental physics and optical devices. Here, we use pump-probe photoemission spectroscopy to study the optically-excited Dirac surface states in the bulk-insulating topological insulator Bi2Te2Se, and reveal optical properties that are in sharp contrast to those of bulk-metallic topological insulators. We observe a gigantic optical life-time exceeding 4 micro-sec for the surface states in Bi2Te2Se, whereas the life-time in most topological insulators such as Bi2Se3 has been limited to a few picoseconds. Moreover, we discover a surface photo-voltage in topological materials, a shift of the chemical potential of the Dirac surface states, as large as 100 mV. Our results demonstrate a rare platform to study charge excitation and relaxation in energy and momentum space in a two dimensional quantum system.

cond-mat.mes-hall↗

arXiv2015

Non-universal weak antilocalization effect in cubic topological Kondo insulators

We study the quantum correction to conductivity on the surface of cubic topological Kondo insulators with multiple Dirac bands. We consider the model of time-reversal invariant disorder which induces the scattering of the electrons within the Dirac bands as well as between the bands. When only intraband scattering is present we find three long-range diffusion modes which lead to weak antilocalization correction to conductivity, which remains independent of the microscopic details such as Fermi velocities and relaxation times. Interband scattering gaps out two diffusion modes leaving only one long-range mode. We find that depending on the value of the phase coherence time, either three or only one long-range diffusion modes contribute to weak localization correction rendering the quantum correction to conductivity non-universal. We provide an interpretation for the results of the recent transport experiments on samarium hexaboride where weak antilocalization has been observed.

cond-mat.str-el↗

arXiv2015

Strong correlation effects in a two-dimensional Bose gas with quartic dispersion

Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of band structure can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jiménez-Garcia, and I. B. Spielman, Nature $\textbf{471}$, 83 (2011)], in the regime where the lower band dispersion has the form $\varepsilon_{\textbf{k}} \sim k_{x}^{4}/4+k_{y}^{2}+\ldots$, or using the shaken lattice scheme of Parker $\textit{et al.}$ [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics $\textbf{9}$, 769 (2013)]. We numerically compare the ground state energies of the mean-field Bose-Einstein condensate (BEC) and various trial wave-functions, where bosons avoid each other at short distances. We discover that, at low densities, several types of strongly correlated states have an energy per particle ($ε$), which scales with density ($n$) as $ε\sim n^{4/3}$, in contrast to $ε\sim n$ for the weakly interacting Bose gas. These competing states include a Wigner crystal, quasi-condensates described in terms properly symmetrized fermionic states, and variational wave-functions of Jastrow type. We find that one of the latter has the lowest energy among the states we consider. This Jastrow-type state has a strongly reduced, but finite condensate fraction, and true off-diagonal long range order, which suggests that the ground state of interacting bosons with quartic dispersion is a strongly-correlated condensate reminiscent of superfluid Helium-4. Our results show that even for weakly-interacting bosons in higher dimensions, one can explore the crossover from a weakly-coupled BEC to a strongly-correlated condensate by simply tuning the single particle dispersion or density.

cond-mat.quant-gas↗

arXiv2015

Topological Kondo Insulators

This article reviews recent theoretical and experimental work on a new class of topological material - topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f-electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in Samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states.

cond-mat.str-el↗

arXiv2015

Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator

Topological Kondo insulators are strongly correlated materials, where itinerant electrons hybridize with localized spins giving rise to a topologically non-trivial band structure. Here we use non-perturbative bosonization and renormalization group techniques to study theoretically a one-dimensional topological Kondo insulator. It is described as a Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel - a strongly correlated version of the prototypical Tamm-Shockley model. We derive and solve renormalization group equations at two-loop order in the Kondo parameter, and find that, at half-filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a non-interacting conduction band (Hubbard parameter $U=0$). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-$1$ chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-$1/2$ end states for chains with open boundary conditions. Our analysis allows to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.

cond-mat.str-el↗

arXiv2015

Moving solitons in a one-dimensional fermionic superfluid

A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kink-like profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The "inertial" and "gravitational" masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent to the observed behavior of a soliton-like texture in related experiments in cold fermion gases [T. Yefsah et al., Nature 499, 426, (2013)]. Furthermore, we calculate the full non-linear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong non-linearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the non-linear soliton spectrum in superfluids.

cond-mat.quant-gas↗

arXiv2015

Charged skyrmions on the surface of a topological insulator

We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at the skyrmion radius, where out of plane magnetization vanishes. This confinement can result in charging of the skyrmion texture. The presence of bound states is robust in an external magnetic field, which is needed to stabilize skyrmions. It is expected that for relevant experimental parameters skyrmions will have a few bound states that can be tuned using an external magnetic field. We argue that these charged skyrmions can be manipulated directly by an electric field, with skyrmion mobility proportional to the number of bound states at the skyrmion radius. Coupling skyrmionic thin films to a TI surface can provide a more direct and efficient way of controlling skyrmion motion in insulating materials. This provides a new dimension in the study of skyrmion manipulation.

cond-mat.mes-hall↗

arXiv2015

Quantum interference phenomena in the Casimir effect

We propose a definitive test of whether plates involved in Casimir experiments should be modeled with ballistic or diffusive electrons--a prominent controversy highlighted by a number of conflicting experiments. The unambiguous test we propose is a measurement of the Casimir force between a disordered quasi-2D metallic plate and a three-dimensional metallic system at low temperatures, in which disorder-induced weak localization effects modify the well-known Drude result in an experimentally tunable way. We calculate the weak localization correction to the Casimir force as a function of magnetic field and temperature and demonstrate that the quantum interference suppression of the Casimir force is a strong, observable effect. The coexistence of weak localization suppression in electronic transport and Casimir pressure would lend credence to the Drude theory of the Casimir effect, while the lack of such correlation would indicate a fundamental problem with the existing theory. We also study mesoscopic disorder fluctuations in the Casimir effect and estimate the width of the distribution of Casmir energies due to disorder fluctuations.

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