arXiv subjects

M. Pletyukhov

Publications and source records attributed to M. Pletyukhov.

At least 19 recordsLinked to original sources

arXiv2021

Quantitative analysis of interaction effects in generalized Aubry-Andŕe-Harper models

We present a quantitative analysis of two-particle interaction effects in generalized, one-dimensional Aubry-André-Harper models with the Fermi energy placed in one of the band gaps. We investigate systems with periodic as well as open boundary conditions; for the latter focusing on the number of edge states and the boundary charge. Both these observables are important for the classification of noninteracting topological systems. In our first class of models the unit cell structure stems from periodically modulated single-particle parameters. In the second it results from the spatial modulation of the two-particle interaction. For both types of models, we find that the single-particle band gaps are renormalized by the interaction in accordance with expectations employing general field theoretical arguments. While interaction induced effective edge states can be found in the local single-particle spectral function close to a boundary, the characteristics of the boundary charge are not modified by the interaction. This indicates that our results for the Rice-Mele and Su-Schriefer-Heeger model [Phys. Rev. B 102, 085122 (2020)] are generic and can be found in lattice models with more complex unit cells as well.

cond-mat.str-el↗

arXiv2020

The interacting Rice-Mele model: bulk and boundaries

We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we firstly compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. The boundary charge is fully determined by bulk properties indicating a bulk-boundary correspondence. In a large parameter regime it agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Secondly, we investigate the robustness of our results towards two-particle interactions. To resum the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the boundary charge are unaltered and can be understood from the renormalized bulk properties, elevating the bulk-boundary correspondence to the interacting regime. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.

cond-mat.str-el↗

arXiv2019

Investigating the roots of the nonlinear Luttinger liquid phenomenology

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

cond-mat.str-el↗

arXiv2013

Magnetic field effects on the finite-frequency noise and ac conductance of a Kondo quantum dot out of equilibrium

We present analytic results for the finite-frequency current noise and the nonequilibrium ac conductance for a Kondo quantum dot in presence of a magnetic field. Using the real-time renormalization group method, we determine the line shape close to resonances and show that while all resonances in the ac conductance are broadened by the transverse spin relaxation rate, the noise at finite field additionally involves the longitudinal rate as well as sharp kinks resulting in singular derivatives. Our results provide a consistent theoretical description of recent experimental data for the emission noise at zero magnetic field, and we propose the extension to finite field for which we present a detailed prediction.

cond-mat.str-el↗

arXiv2013

Scaling of the Kondo zero bias peak in a hole quantum dot at finite temperatures

We have measured the zero bias peak in differential conductance in a hole quantum dot. We have scaled the experimental data with applied bias and compared to real time renormalization group calculations of the differential conductance as a function of source-drain bias in the limit of zero temperature and at finite temperatures. The experimental data show deviations from the T=0 calculations at low bias, but are in very good agreement with the finite T calculations. The Kondo temperature T_K extracted from the data using T=0 calculations, and from the peak width at 2/3 maximum, is significantly higher than that obtained from finite T calculations.

cond-mat.str-el↗

arXiv2013

Oscillatory dynamics and non-markovian memory in dissipative quantum systems

The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (1) the oscillatory dynamics close to a coherent-to-incoherent transition is surprisingly different from the one of the classical damped harmonic oscillator and that (2) non-markovian memory plays a prominent role in the time evolution after a quantum quench.

cond-mat.str-el↗

arXiv2012

A renormalization-group analysis of the interacting resonant level model at finite bias: Generic analytic study of static properties and quench dynamics

Using a real-time renormalization group method we study the minimal model of a quantum dot dominated by charge fluctuations, the two-lead interacting resonant level model, at finite bias voltage. We develop a set of RG equations to treat the case of weak and strong charge fluctuations, together with the determination of power-law exponents up to second order in the Coulomb interaction. We derive analytic expressions for the charge susceptibility, the steady-state current and the conductance in the situation of arbitrary system parameters, in particular away from the particle-hole symmetric point and for asymmetric Coulomb interactions. In the generic asymmetric situation we find that power laws can be observed for the current only as function of the level position (gate voltage) but not as function of the voltage. Furthermore, we study the quench dynamics after a sudden switch-on of the level-lead couplings. The time evolution of the dot occupation and current is governed by exponential relaxation accompanied by voltage-dependent oscillations and characteristic algebraic decay.

cond-mat.str-el↗

arXiv2010

Non-equilibrium current and relaxation dynamics of a charge-fluctuating quantum dot

We study the steady-state current in a minimal model for a quantum dot dominated by charge fluctuations and analytically describe the time evolution into this state. The current is driven by a finite bias voltage V across the dot, and two different renormalization group methods are used to treat small to intermediate local Coulomb interactions. The corresponding flow equations can be solved analytically which allows to identify all microscopic cutoff scales. Exploring the entire parameter space we find rich non-equilibrium physics which cannot be understood by simply considering the bias voltage as an infrared cutoff. For the experimentally relevant case of left-right asymmetric couplings, the current generically shows a power-law suppression for large V. The relaxation dynamics towards the steady state features characteristic oscillations as well as an interplay of exponential and power-law decay.

cond-mat.mes-hall↗

arXiv2010

Comparative study of theoretical methods for nonequilibrium quantum transport

We present a detailed comparison of three different methods designed to tackle nonequilibrium quantum transport, namely the functional renormalization group (fRG), the time-dependent density matrix renormalization group (tDMRG), and the iterative summation of real-time path integrals (ISPI). For the nonequilibrium single-impurity Anderson model (including a Zeeman term at the impurity site), we demonstrate that the three methods are in quantitative agreement over a wide range of parameters at the particle-hole symmetric point as well as in the mixed-valence regime. We further compare these techniques with two quantum Monte Carlo approaches and the time-dependent numerical renormalization group method.

cond-mat.mes-hall↗

arXiv2010

Functional renormalization group study of the interacting resonant level model in and out of equilibrium

We investigate equilibrium and steady-state non-equilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width ~Γvia a Coulomb interaction U and a hybridization t'. In order to study the effects of finite bias voltages beyond linear response, a generalization of the functional renormalization group to Keldysh frequency space is employed. Being mostly unexplored in the context of quantum impurity systems out of equilibrium, we benchmark this method against recently-published time-dependent density matrix renormalization group data. We thoroughly investigate the scaling limit Γ\to\infty characterized by the appearance of power laws. Most importantly, at the particle-hole symmetric point the steady-state current decays like J ~ V^{-α_J} as a function of the bias voltage V>>t', with an exponent α_J(U) that we calculate to leading order in the Coulomb interaction strength. In contrast, we do not observe a pure power-law (but more complex) current-voltage-relation if the energy εof the resonant level is pinned close to either one of the chemical potentials \pm V/2.

cond-mat.str-el↗

arXiv2008

Tunable Aharonov-Anandan phase in transport through mesoscopic hole rings

We present a theoretical study of spin-3/2 hole transport through mesoscopic rings, based on the spherical Luttinger model. The quasi-one-dimensional ring is created in a symmetric two-dimensional quantum well by a singular-oscillator potential for the radial in-plane coordinate. The quantum-interference contribution to the two-terminal ring conductance exhibits an energy-dependent Aharonov-Anandan phase, even though Rashba and Dresselhaus spin splittings are absent. Instead, confinement-induced heavy-hole - light-hole mixing is found to be the origin of this phase, which has ramifications for magneto-transport measurements in gated hole rings.

cond-mat.mes-hall↗

arXiv2007

Charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies

We analytically evaluate charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies. On the basis of our exact expressions we discuss the accuracy of the long-wavelength and the quasiclassical approximations. We also derive the static limit of spin susceptibilities and demonstrate, in particular, how the Kohn-like anomalies in their derivatives are related to the spin-orbit modification of the Ruderman-Kittel-Kasuya-Yosida interaction. Taking into account screening and exchange effects of the Coulomb interaction, we describe the collective charge and spin density excitation modes which appear to be coupled due to nonvanishing spin-charge response function.

cond-mat.mes-hall↗

arXiv2007

Crossover from diffusive to non-diffusive dynamics in the two-dimensional electron gas with Rashba spin-orbit coupling

We present the calculation of the density matrix response function of the two-dimensional electron gas with Rashba spin-orbit interaction, which is applicable in a wide range of parameters covering the diffusive and non-diffusive, the dirty and the clean limits. A description of the crossover between the different regimes is thus provided as well. On the basis of the derived microscopic expressions we study the propagating charge and spin-polarization modes in the clean, non-diffusive regime, which is accessible in the modern experiments.

cond-mat.mes-hall↗

arXiv2006

Tunneling conductance of a mesoscopic ring with spin-orbit coupling and Tomonaga-Luttinger interaction

We study the tunneling current through a mesoscopic two-terminal ring with spin-orbit coupling, which is threaded by a magnetic flux. The electron-electron interaction in the ring is described in terms of a Tomonaga-Luttinger model which also allows us to account for a capacitive coupling between the ring and the gate electrode. In the regime of weak tunneling, we describe how, at temperatures lower than the mean level spacing, the peak positions of the conductance depend on magnetic flux, spin-orbit coupling strength, gate voltage, charging energy, and interaction parameters (charge and spin velocity and stiffness).

cond-mat.mes-hall↗

arXiv2006

Screening properties of the two-dimensional electron gas with spin-orbit coupling

We study screening properties of the two-dimensional electron gas with Rashba spin-orbit coupling. Calculating the dielectric function within the random phase approximation, we describe the new features of screening induced by spin-orbit coupling, which are the extension of the region of particle-hole excitations and the spin-orbit-induced suppression of collective modes. The required polarization operator is calculated in an analytic form without any approximations. Carefully deriving its static limit, we prove the absence of a small-$q$ anomaly at zero frequency. On the basis of our results at finite frequencies we establish the new boundaries of the particle-hole continuum and calculate the SO-induced lifetime of collective modes such as plasmons and longitudinal optical phonons. According to our estimates, these effects can be resolved in inelastic Raman scattering. We evaluate the experimentally measurable dynamic structure factor and establish the range of parameters where the described phenomena are mostly pronounced.

cond-mat.mes-hall↗

arXiv2005

Screening in the two-dimensional electron gas with spin-orbit coupling

We study the interplay between electron-electron interaction and Rashba spin-orbit coupling in the two-dimensional electron gas. Using the random phase approximation we predict new screening properties of the electron gas which result in extension of the region of particle-hole excitations and in spin-orbit induced suppression of collective modes. In particular, we observe that the spin-orbit coupling gives a finite lifetime to plasmons and longitudinal optical phonons, which can be resolved in inelastic Raman scattering. We evaluate the experimentally measurable dynamic structure factor and estimate the range of parameters where the described phenomena are mostly pronounced.

cond-mat.mes-hall↗

arXiv2005

Competing effects of interactions and spin-orbit coupling in a quantum wire

We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.

cond-mat.mes-hall↗

arXiv2004

Persistent currents in multicomponent Tomonaga-Luttinger liquid: application to mesoscopic semiconductor ring with spin-orbit interaction

We study persistent currents in semiconductor ballistic rings with spin-orbit Rashba interaction. We use as a working model the multicomponent Tomonaga-Luttinger liquid which arises due to the nonparabolic dispersion relations of electrons in the rings with rather strong spin-orbit coupling. This approach predicts some new characteristic features of persistent currents, which may be observed in experimental studies of semiconductor ballistic rings.

cond-mat.mes-hall↗