arXiv subjects

D. N. Aristov

Publications and source records attributed to D. N. Aristov.

At least 19 recordsLinked to original sources

arXiv2026

Finite-frequency conductivity of nonlinear Luttinger liquid in smooth random potential

We analyze the uniform conductivity of a one-dimensional degenerate fermion system placed in a random disorder potential so smooth that backward scattering can be neglected. We use the nonlinear Luttinger liquid model to consider effects of both interaction and the curvature of fermionic dispersion. The finite frequency conductivity, calculated in the lowest order of disorder potential, consists of two parts. First one is the elastic contribution, largely independent of temperature and interaction. Second one is the inelastic contribution, strongly dependent on temperature and frequency and appearing upon simultaneous presence of curvature, disorder and interaction. We argue that apart from such finite frequency conductivity, there should always remain the $δ$-function peak of conductivity at zero frequency, whose weight is weakly dependent on the disorder.

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arXiv2025

Shot noise in Aharonov-Bohm interferometers: Comparison of helical and conventional setups

We study tunneling transport through quantum Aharonov-Bohm (AB) interferometers and demonstrate that interference effects strongly modify shot noise of the current. We discuss in detail two simplest setups: conventional single-channel spinless interferometer and interferometer formed by helical edge states of two-dimensional topological insulator. We demonstrate that both in the conventional and the helical case the interference dramatically changes the Fano factor and its magnetic field dependence. For weak tunneling coupling, the Fano factor of both setups exhibits a periodic series of sharp AB peaks depending on the magnetic flux piercing the system. Our key finding is that the Fano factor in the helical interferometer provides information about the presence of backscattering defects violating topological protection. In particular, the amplitude of AB peaks in the helical setup is proportional to the strength of the defect in contrast to conventional setup, where peaks have finite amplitude even in the ballistic case.

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arXiv2025

A non-magnetic mechanism of backscattering in helical edge states

We study interaction-induced backscattering mechanism for helical edge states of a two-dimensional topological insulator which is tunnel-coupled to a puddle located near the edge channel. The mechanism does not involve inelastic scattering and is due to the zero-mode fluctuations in a puddle. We discuss in detail a simple model of a puddle - a cavity in the bulk of the topological insulator. Such a cavity also has helical edge states with tunneling coupling to helical states encompassing the topological insulator. We analyze effect of the edge current in the puddle. Although averaged value of this current is equal to zero, its zero-mode fluctuations act, in the presence of electron-electron interaction, similar to magnetic flux thus allowing backscattering processes, which involve tunneling through the puddle. Rectification of these fluctuations leads to a finite probability of backscattering. This effect is further enhanced due to dephasing process which is also dominated by zero-mode fluctuations. Remarkably, for temperature exceeding level spacing in the puddle, the rate of backscattering does not depend on temperature in a good agreement with recent experiments.

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arXiv2025

Topological transition in spectrum of skyrmion crystal with uniaxial anisotropy

The band structure of elementary excitations of skyrmion crystal in thin ferromagnetic film with Dzyaloshinskii-Moriya interaction and uniaxial magnetic anisotropy under external magnetic field is studied. In the absence of anisotropy there is a topological transition in the spectrum of skyrmion crystal: the gap between breathing and counter-clock-wise modes closes, which is accompanied by changes of Berry curvature sign of these bands. In this work we demonstrate that such topological transition exists in some range of the uniaxial anisotropy values. We present a phase diagram showing that the value of the field of topological transition is higher in the easy-plane domain and lower in the easy-axis domain of anisotropy.

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arXiv2025

Magnon edge states of skyrmion crystal in non-uniform magnetic field

A regular lattice of magnetic skyrmions is the ground state of thin ferromagnetic films with Dzyaloshinskii-Moriya interaction in a relatively wide range of external magnetic fields. It was previously theoretically shown that upon the increase of magnetic field a topological transition in the magnon spectrum of such skyrmion crystal (SkX) may occur. Non-uniform magnetic field may lead to localized magnon states emerging at the interface between two half-planes of SkX. Using semiclassical quantization and the stereographic projection approach, we study such appearing edge states both in a full band structure calculation and in simplified effective model. The latter effective model described by extended Dirac equation is applicable to two relevant magnon bands near $Γ$ point. We show that both the chirality of emerging edge states and the degree of its localization at the interface is controlled by magnetic field profile. We demonstrate that the localization length may be as small as a few inter-skyrmion distances.

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arXiv2024

Stability boundaries of the skyrmion phase in non-centrosymmetric ferromagnets with Dzyaloshinskii-Moriya interaction

Stability boundaries of the skyrmion lattice in non-centrosymmetric bulk ferromagnets with the Dzyaloshinskii-Moriya interaction in external magnetic field are discussed. We compare the classical energies of the spin configuration of the conical helix and skyrmion lattice within the framework of the stereographic projection approach. It is well known that at low temperatures the skyrmion lattice loses energetically to the conical helix in the entire range of fields, $0 < H < H_{c2}$, where $H_{c2}$ is the transition field to the polarized collinear phase, and $gμ_B H_{c2} \ll T_c$. We show that taking into account the dipole interaction does not qualitatively change the situation. However, the possibility of fluctuations in the absolute value of the equilibrium local magnetization in the Ginzburg-Landau functional leads, with increasing temperature, $T$, to the skyrmion lattice becoming energetically more favorable than the conical helix in a certain range of fields. We show that it occurs already in the first order of small parameter, $\propto gμ_B H_{c2}/|T-T_c|$, at the level of mean field theory.

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arXiv2023

Tunable helical crystals

We consider a superlattice formed by tunnel-connected identical holes, periodically placed in a two-dimensional topological insulator. We study tunneling transport through helical edges of these holes and demonstrate that the band structure of such helical crystal can be controlled by both gate electrodes and external magnetic filed. For integer and half-integer values of dimensionless magnetic flux through the holes, the spectrum possesses Dirac points whose positions and velocities can be tuned by gates. The deviation of magnetic flux from these special values by $δϕ$ makes the Dirac cones massive, with the gap value $Δ\propto |δϕ|$. At certain gate-dependent values of $δϕ$ different Dirac points converge to a double Dirac point and then disappear with further increase of $δϕ.$ Interaction between carriers may lead to strong renormalization of parameters $α$ and $β$ controlling total tunnel coupling between holes and spin flip tunneling processes, respectively. We plot the renormalization flow in the plane $(α,β)$ and demonstrate multicritical behavior of the crystal -- there is a multicritical fully unstable fixed point separating three different phases: independent rings, independent shoulders, and perfect spin-flip channels. We also find that defects in the crystal may lead to a formation of topologically protected qubits which are not destroyed by temperature and can be also manipulated both by gates and by magnetic field. The possibility of purely electrical high-temperature control of the qubits opens a wide avenue for applications in the area of quantum computing.

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arXiv2023

Effective Hamiltonian of topologically protected qubit in a helical crystal

We study a superlattice formed by tunnel-coupled identical antidots periodically situated in a two-dimensional topological insulator placed in a magnetic field. The superlattice spectrum can be controlled by gate electrodes or by changing the magnetic flux through the antidots. We demonstrate that a topologically protected qubit appears at the boundary between two regions with different fluxes. The qubit properties depend on the value of the flux jump on the boundary and can be controlled by the gate voltage. We derive the effective Hamiltonian of such a qubit and analyze the dependence of its properties on the main parameters of the superlattice: the tunnel coupling between antidots, and the probability of jumps with the spin flip.

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arXiv2023

Magnon topological transition in skyrmion crystal

We study the magnon spectrum in skyrmion crystal formed in thin ferromagnetic films with Dzyalosinskii-Moria interaction in presence of magnetic field. Focusing on two low-lying observable magnon modes and employing stereographic projection method, we develop a theory demonstrating a topological transition in the spectrum. Upon the increase of magnetic field, the gap between two magnon bands closes, with the ensuing change in the topological character of both bands. This phenomenon of gap closing, if confirmed in magnetic resonance experiments, may deserve further investigation by thermal Hall conductivity experiments.

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arXiv2023

Goldstone mode of Skyrmion Crystal

We discuss the Goldstone mode of skyrmion crystal in a model of two-dimenssional ferromagnet with Dzyaloshinskii-Moriya interaction in magnetic field. We use stereographic projection approach to construct skyrmion crystal and consider skyrmion's displacement field. The small overlap of the individual skyrmion images restricts the potential energy to the interaction of nearest neighboring displacements. The closed form of the Goldstone mode dispersion is found and its dependence on the magnetic field is studied. We use semiclassical quantization to define the Green's function and show that the propagation of displacements through the crystal changes its tensorial form from isotropic to anisotropic one at large distances.

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arXiv2022

Dynamical susceptibility of Skyrmion crystal

Using stereographic projection approach we develop a theory for calculation of dynamical susceptibility tensor of Skyrmion crystals (SkX), formed in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and in the external magnetic field. Staying whenever possible within analytical framework, we employ the model anzats for static SkX configuration and discuss small fluctuations around it. The obtained formulas are numerically analyzed in the important case of uniform susceptibility, accessible in magnetic resonance (MR) experiments. We show that, in addition to three characteristic MR frequencies discussed earlier both theoretically and experimentally, one should also expect several resonances of smaller amplitude at somewhat higher frequencies.

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arXiv2021

Coherent spin transport through helical edge states of topological insulator

We study coherent spin transport through helical edge states of topological insulator tunnel-coupled to metallic leads. We demonstrate that unpolarized incoming electron beam acquires finite polarization after transmission through such a setup provided that edges contain at least one magnetic impurity. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum magnetic field-tunable contribution to the polarization, which shows sharp identical Aharonov-Bohm resonances as a function of magnetic flux - with the period $hc/2e$ - and survives at relatively high temperature. We demonstrate that this tunneling interferometer can be described in terms of ensemble of flux-tunable qubits giving equal contributions to conductance and spin polarization. The number of active qubits participating in the charge and spin transport is given by the ratio of the temperature and the level spacing. The interferometer can effectively operate at high temperature and can be used for quantum calculations. In particular, the ensemble of qubits can be described by a single Hadamard operator. The obtained results open wide avenue for applications in the area of quantum computing.

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arXiv2021

Magnon band structure of skyrmion crystals and stereographic projection approach

Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The topologically non-trivial ground state of SkX is described in stereographic projection by the complex valued function with simple poles at skyrmions' positions. We use the earlier proposed ansatz for this ground state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure of tight-binding form in accordance with previously known results. There are two sets of bands, one set with a flat dispersion, topologically trivial and rapidly evolving with magnetic field. Another set is robust to magnetic field, characterized by pronounced dispersion and with the Berry curvature which may be sign-reversal in the Brillouin zone. The developed theory can be straightforwardly generalized for the analysis of magnetic dynamics in topological spin structures of other types.

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arXiv2021

Triple helix vs. skyrmion lattice in two-dimensional non-centrosymmetric magnets

It is commonly assumed that a lattice of skyrmions, emerging in two-dimensional non-centrosymmetric magnets in external magnetic fields, can be represented as a sum of three magnetic helices. In order to test this assumption we compare two approaches to a description of regular skyrmion structure. We construct (i) a lattice of Belavin-Polyakov-like skyrmions within the stereographic projection method, and (ii) a deformed triple helix defined with the use of elliptic functions. The estimates for the energy density and magnetic profiles show that these two ansatzes are nearly identical at zero temperature for intermediate magnetic fields. However at higher magnetic fields, near the transition to topologically trivial uniform phase, the stereographic projection method is preferable, particularly, for the description of disordered skyrmion liquid phase. We suggest to explore the intensities of the secondary Bragg peaks to obtain the additional information about the magnetic profile of individual skyrmions. We estimate these intensities to be several percents of the main Bragg peak at high magnetic fields.

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arXiv2021

Spin and charge transport through helical Aharonov-Bohm interferometer with strong magnetic impurity

We discuss transport through an interferometer formed by helical edge states of the quantum spin Hall insulator. Focusing on effects induced by a strong magnetic impurity placed in one of the arms of interferometer, we consider the experimentally relevant case of relatively high temperature as compared to the level spacing. We obtain the conductance and the spin polarization in the closed form for arbitrary tunneling amplitude of the contacts and arbitrary strength of the magnetic impurity. We demonstrate the existence of quantum effects which do not show up in previously studied case of weak magnetic disorder. We find optimal conditions for spin filtering and demonstrate that the spin polarization of outgoing electrons can reach 100%.

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arXiv2020

Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium

The renormalization of conductances in a Y junction of spinless Luttinger-liquid wires additionally coupled to acoustic longitudinal phonons is investigated in fermionic representation. This system corresponds to geometry of a tunneling experiment and exhibits the interplay between the Coulomb repulsion and the attractive retarded interaction mediated by phonons. The retardation effects related to the propagation of phonons through the junction with arbitrary transmission and reflection amplitudes are taken into account. The appearing logarithmic corrections to conductances of the junction are treated in a renormalization group approach, and scaling exponents are calculated up to infinite order in the interaction after RPA-type summation. The fixed points and corresponding scaling exponents are considered in various non-equilibrium regimes. We show that the boundary exponent and the bulk anomalous dimension of fermion operator are characterized by two different Luttinger parameters, referring to the main wire, thanks to non-local character of phonon-mediated interaction. In the limiting case of the junction of only two wires, the scaling exponents found by our method are in exact correspondence with previous bosonization analysis.

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arXiv2019

Emergent chirality in multi-lead Luttinger-liquid junctions out of equilibrium

We study charge transport through $N$-lead junctions ($N\geq 3$) of spinless Luttinger liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle $S$ matrix of the junction, we find that the bias voltage $V$ applied---even symmetrically---to the main wire generates a current proportional to $|V|$ in the tip wire. We identify two mechanisms of this nonequilibrium-induced "emergent chirality" in a setup characterized by the time-reversal and parity symmetric Hamiltonian of the junction. These are: (i) the emergence of an effective magnetic flux, which breaks time-reversal symmetry, and (ii) the emergence of parity-breaking asymmetry of the setup, both proportional to the interaction strength and the sign of the voltage. The current in the tip wire generated by mechanism (i) is reminiscent of the Hall current in the linear response of a system the Hamiltonian of which breaks time-reversal symmetry; however, in the absence of any magnetic field or a local magnetic moment. Similarly, mechanism (ii) can be thought of as an emergent "photogalvanic effect"; however, in the presence of inversion symmetry within the main wire. The nonequilibrium chirality implies a rectification of the current in the tip when the main wire is biased by $\it ac$ voltage.

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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.

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