arXiv subjects

D. B. Gutman

Publications and source records attributed to D. B. Gutman.

At least 19 recordsLinked to original sources

arXiv2021

Anomalous Hydrodynamics in One Dimensional Electronic Fluid

We construct multi-mode viscous hydrodynamics for one dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In a four-mode regime, all modes are ballistic and acquire KPZ-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to $ω^{-1/3}$ scaling of its real part. In a three-mode regime, the system is in the universality class of classical viscous fluid[9,24]. Self-interaction of the sound modes results in KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to $ω^{-1/3}$ scaling of heat conductivity.

cond-mat.mes-hall↗

arXiv2019

Thermal Transport in One Dimensional Electronic Fluid

We study thermal conductivity for one-dimensional electronic fluid. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than bosonic Umklapp time, the momentum of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to $T / iω$. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by L{é}vy flights of low-momentum bosons that lead to a fractional scaling, $ω^{-\frac{1}{3}}$ and $L^{1/3}$, of heat conductivity with the frequency $ω$ and system size $L$ respectively.

cond-mat.str-el↗

arXiv2018

Edge states in a two-dimensional non-symmorphic semimetal

Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of Dirac materials, protected by non-symmorphic symmetries was recently proposed by Young and Kane [1]. By breaking of time reversal or inversion symmetry one can split the Dirac cones into Weyl nodes. The later are characterized by local Chern numbers, that makes them two-dimensional analogs of Weyl semimetals. We find that the formation of the Weyl nodes is accompanied by an emergence of one-dimensional surface states, similar to Fermi arcs in Weyl semimetals and edge states in two-dimensional graphene. We explore these states for a quasi-one-dimensional non-symmorphic ribbon. The type and strength of applied deformation control the location and Weyl nodes and their composition. This determines the properties of emerging edge states. The sensitivity of these edge states to the external deformations makes non-symmorphic materials potentially useful as a new type of electromechanical sensors.

cond-mat.mes-hall↗

arXiv2018

Interplay between intrinsic and emergent topological protection on interacting helical modes

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent $\mathbb{Z}_{2}$ topological protection, and hence a zero-temperature conductance of $G=e^2/h$. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase, there is zero conductance $G=0$ at zero-temperature. The other phase displays enhanced topological properties, with the neutral sector described by a massive version of $\mathbb{Z}_{3}$ parafermions. In this phase, the system at low energies displays an emergent $\mathbb{Z}_3$ symmetry, which is not present in the lattice model, and has a topologically protected zero-temperature conductance of $G=3e^2/h$. This state is an example of a dynamically enhanced symmetry protected topological state.

cond-mat.str-el↗

arXiv2017

Shot noise in Weyl semimetals

We study the effect of inelastic processes on the magneto-transport of a quasi-one dimensional Weyl semi-metal, using a modified Boltzmann-Langevin approach. The magnetic field drives a crossover to a ballistic regime in which the propagation along the wire is dominated by the chiral anomaly, and the role of fluctuations inside the sample is exponentially suppressed. We show that inelastic collisions modify the parametric dependence of the current fluctuations on the magnetic field. By measuring shot noise as a function of a magnetic field, for different applied voltage, one can estimate the electron-electron inelastic length $l_{\rm ee}$.

cond-mat.mes-hall↗

arXiv2016

Phase diagram of two interacting helical states

We consider two coupled time reversal invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is non-zero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intra-edge interaction is stronger than the inter-edge interaction, the state is characterised as a spin-nematic phase. However in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. Firstly, the gap protects the conducting phase against localization by weak nonmagnetic impurities; and secondly the protected phase hosts localized zero modes on ends of the edge that may be created by sufficiently strong non-magnetic impurities.

cond-mat.mes-hall↗

arXiv2016

Manipulation of Majorana states in X-junction geometries

We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, $2α$, accumulated during the manipulation. We construct simple protocols for the variety of values of $α$, including $π/8$ needed for the purposes of quantum computation. Although the manipulations in general X-junction geometry are not topologically protected, they may prove to be a feasible compromise for aims of quantum computation.

cond-mat.mes-hall↗

arXiv2016

Energy transport in the Anderson insulator

We study the heat conductivity in Anderson insulators in the presence of power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal conductivity. For physically relevant cases of 2D and 3D spin systems with $1/r^3$ dipole-dipole interaction (originating from the conventional $1/r$ Coulomb interaction between electrons), the found thermal conductivity $κ$ scales with temperature as $κ\propto T^3 $ and $κ\propto T^{4/3}$, respectively. Our results may be of relevance also to other realizations of random spin Hamiltonians with long-range interactions.

cond-mat.dis-nn↗

arXiv2016

Interaction induced topological protection in one-dimensional conductors

We discuss two one-dimensional model systems -- the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder.

cond-mat.mes-hall↗

arXiv2016

Korshunov instantons out of equilibrium

Zero-dimensional dissipative action possesses non-trivial minima known as Korshunov instantons. They have been known so far only for imaginary time representation that is limited to equilibrium systems. In this work we reconstruct and generalise Korshunov instantons using real-time Keldysh approach. This allows us to formulate the dissipative action theory for generic non-equilibrium conditions. Possible applications of the theory to transport in strongly biased quantum dots are discussed..

cond-mat.mes-hall↗

arXiv2016

Pulse propagation in interacting one dimensional Bose liquid

We study wave propagation in interacting Bose liquid, where the short range part of the interaction between atoms is of a hard core type, and its long range part scales with a distance as a power law. The cases of Coulomb, dipole-dipole and Van der Waals interaction are considered. We employ a hydrodynamic approach, based on the exact solution of Lieb-Liniger model, and study the evolution of a density pulse instantly released from a potential trap. We analyze semi-classical Euler and continuity equations and construct the corresponding Riemann invariants. We supplement our analysis with numerical calculations and discuss experimental applications for ultacold atom experiments.

cond-mat.quant-gas↗

arXiv2015

Interaction Protected Topological Insulators with Time Reversal Symmetry

Anderson's localization on the edge of two dimensional time reversal (TR) topological insulator (TI) is studied. For the non-interacting case the topological protection acts accordingly to the $\mathbb{Z}_2$ classification, leading to conducting and insulating phases for odd and even fillings respectively. In the presence of repulsive interaction the phase diagram is notably changed. We show that for sufficiently strong values of the interaction the zero temperature fixed point of the TI is conducting, including the case of even fillings. We compute the boundaries of the conducting phase for various fillings and types of disorder.

cond-mat.str-el↗

arXiv2015

Fractional Coulomb blockade in a coupling controlled metallic quantum dot

We use a novel technique to experimentally explore transport properties through a single metallic nanoparticle with variable coupling to electric leads. For strong dot-lead coupling the conductance is an oscillatory function of the gate voltage with periodicity determined by the charging energy, as expected. For weaker coupling we observe the appearance of additional multi-periodic oscillations of the conductance with the gate voltage. These harmonics correspond to a change of the charge on the dot by a fraction of an electron. This notion is supported by theoretical calculations based on dissipative action theory. Within this framework the multiple periodicity of the conductance oscillations arises due to non-pertubative instanton solutions.

cond-mat.mes-hall↗

arXiv2015

Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory

The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.

cond-mat.str-el↗

arXiv2014

Equilibration in a chiral Luttinger liquid

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperature ("bosonic") and the low-temperature ("fermonic") regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as $k^7T^7$.

cond-mat.str-el↗

arXiv2014

Relaxation in Luttinger liquids: Bose-Fermi duality

We explore the life time of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak-coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant $λ= m^*l^2T$ and the bosonic theory by $λ^{-1}$, where $1/m^*$ and $l$ characterize the curvature of the fermionic and bosonic spectra, respectively, and $T$ is the temperature.

cond-mat.str-el↗

arXiv2013

Dissipationless kinetics of one dimensional interacting fermions

We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a non-linear single-particle spectrum. We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a non-linear transformation which decouples the left- and right-moving excitations. Employing this approach, we investigate the kinetics of the phase space distribution of the quasiparticles and thus determine the time evolution of the density pulse. This allows us to explore a crossover from the essentially free-fermion evolution for weak or short-range interaction to hydrodynamics emerging in the case of sufficiently strong, long-range interaction.

cond-mat.str-el↗

arXiv2012

Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(ε)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish non-equilibrium power-law singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing correlations between left- and right-moving fermions that have left the interaction region.

cond-mat.str-el↗