arXiv subjects

D. N. Aristov

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

At least 37 records · Page 2Linked to original sources

arXiv2018

Towards an effective theory of skyrmion crystals

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of $B, D\neq0$, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by $D$ and $B$. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc.

cond-mat.str-el↗

arXiv2018

Tunneling Aharonov-Bohm interferometer on helical edge states

We discuss transport through interferometer formed by helical edge states tunnel-coupled to metallic leads. We focus on the experimentally relevant case of relatively high temperature as compared to the level spacing and discuss a response of the setup to the external magnetic flux $ϕ$ (measured in units of flux quantum) piercing the area encompassed by edge states. We demonstrate that tunneling conductance of the interferometer is structureless in ballistic case but shows a sharp antiresonances, as a function of magnetic flux $ϕ$ - with the period 1/2 - in the presence of magnetic impurity. We interpret the resonance behavior as a coherent enhancement of backward scattering off magnetic impurity at integer and half-integer values of flux, which is accompanied by suppression of the effective scattering at other values of flux. Both enhancement and suppression are due to the interference of processes with multiple returns to magnetic impurity after a number of clockwise and counterclockwise revolutions around setup. This phenomenon is similar to the well-known weak-localization-induced enhancement of backscattering in disordered systems. The quantum correction to the tunneling conductance is shown to be proportional to flux-dependent "ballistic Cooperon". The obtained results can be used for flux-tunable control of the magnetic disorder in Aharonov-Bohm interferometers built on helical edge states.

cond-mat.mes-hall↗

arXiv2018

Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

We develop the renormalization group theory of the conductances of N-lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group $β$ functions are derived up to second order.

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↗

arXiv2017

Magnon spectrum in two- and three- dimensional skyrmion crystals

We study the low-energy magnon spectrum of the skyrmion crystal (SkX) ground state, appearing in two-dimensional ferromagnet with Dzyaloshinskii-Moriya interaction and magnetic field. We approximate SkX hexagonal superlattice by a set of overlapping disks, and find the lattice period by minimizing the classical energy density. The determined spectrum of magnons on the disc of optimal radius is stable and only two lowest energy levels can be considered as localized. The subsequent hybridization of these levels in the SkX lattice leads to tight-binding spectrum. The localized character of the lowest magnon states is lost at small and at high fields, which is interpreted as melting of SkX. The classical energy of SkX is slightly above the energy of a single conical spiral, and a consideration of quantum corrections can favor the skyrmion ground state. Extending our analysis to three-dimensional case, we argue that these quantum corrections become more important at finite temperatures, when the average spin value is decreased.

cond-mat.str-el↗

arXiv2017

Y-junction of Luttinger-liquid wires out of equilibrium

We calculate the conductances of a three-way junction of spinless Luttinger-liquid wires as functions of bias voltages applied to three independent Fermi-liquid reservoirs. In particular, we consider the setup that is characteristic of a tunneling experiment, in which the strength of electron-electron interactions in one of the arms of the junction ("tunneling tip") is different from that in the other two arms (which together form a "main wire"). The scaling dependence of the two independent conductances on bias voltages is determined within a fermionic renormalization-group approach in the limit of weak interactions. The solution shows that, in general, the conductances scale with the bias voltages in an essentially different way compared to their scaling with the temperature $T$. Specifically, unlike in the two-terminal setup, the nonlinear conductances cannot be generically obtained from the linear ones by simply replacing $T$ with the "corresponding" bias voltage or the largest one. Remarkably, a finite tunneling bias voltage prevents the interaction-induced breakup of the main wire into two disconnected pieces in the limit of zero $T$ and a zero source-drain voltage.

cond-mat.str-el↗

arXiv2017

Spin-polarized tunneling into helical edge states: asymmetry and conductances

We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In lowest order of tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The helical edge state forbids the backscattering, which leads to the possibility of two stable fixed points in renormalization group sense, in contrast to the Y-junction between the usual quantum wires.

cond-mat.str-el↗

arXiv2016

Stability of a skyrmion and interaction of magnons

The stability of a single Belavin-Polyakov (BP) skyrmion in isotropic Heisenberg ferromagnet is studied. Such skyrmion is higher in energy than the uniform ferromagnetic state and is thus metastable. Starting from the lattice model in two spatial dimensions and using Maleyev-Dyson representation for spin operators, we examine the effects of magnon-magnon interaction for two quantities at $T=0$. First we discuss the self-energy corrections to magnon energy. Second we analyze the two-particle Green's function and possible bound states of two magnons. The simplicity of the model makes possible full analytic treatment of all relevant processes. We found that the magnons remain well-defined quasiparticles with a finite lifetime. The bound states of two magnons are suppressed near the skyrmion, although they are not excluded far away from it. A resonance for the magnons of dilational mode in the vicinity of BP skyrmion is also found, which leads to a redistribution of the spectral weight. We conclude that the BP skyrmion as the classical topological object is not destroyed by quantum fluctuations.

cond-mat.str-el↗

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

Tunneling into and between helical edge states - fermionic approach

We study four-terminal junction of spinless Luttinger liquid wires, which describes either a corner junction of two helical edges states of topological insulators or the tunneling from the spinful wire into the helical edge state. We use the fermionic representation and the scattering state formalism, in order to compute the renormalization group (RG) equations for the linear response conductances. We establish our approach by considering a junction between two possibly non-equivalent helical edge states and find an agreement with the earlier analysis of this situation. Tunneling from the tip of the spinful wire to the edge state is further analyzed which requires some modification of our formalism. In the latter case we demonstrate i) the existence of both fixed lines and conventional fixed points of RG equations, and ii) certain proportionality relations holding for conductances during renormalization. The scaling exponents and phase portraits are obtained in all cases.

cond-mat.str-el↗

arXiv2015

Magnon spectrum in ferromagnets with a skyrmion

The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is performed with a single skyrmion in the ground state. We employ the ideas of semiclassical quantization method, duly modified for the use of the lattice model and Maleyev-Dyson boson representation of spin operators. The resulting Schrödinger equation for magnons describes the dispersion and wave functions of spin-wave excitations with strictly non-negative spectrum. In contrast to usual ferromagnet, we demonstrate the existence of three zero modes, corresponding to conformal symmetries spontaneously violated by the skyrmion configuration.

cond-mat.str-el↗

arXiv2015

Ambiguity in renormalization of X-junction between Luttinger liquid wires

We study four-lead junction of semi-infinite wires by using fermionic representation in the scattering state formalism. The model of spinless fermions with short-range Luttinger liquid type interaction is used. We find the renormalization group (RG) equations for the conductances of the system in the first order of fermionic interaction. In contrast to the well-known cases of two-lead and three-lead junctions, we show that the RG equations cannot be expressed solely in terms of conductances. The appearing ambiguity is resolved by choosing a certain sign defined at the level of S-matrix, but hidden in conductances. The origin of this Z_2 symmetry is traced back to the particle-hole symmetry of our Hamiltonian. We demonstrate two distinct RG flows from any point in the space of conductances. The scaling exponents at the fixed points are not affected by these observations.

cond-mat.str-el↗

arXiv2014

Transport properties of a two-lead Luttinger liquid junction out of equilibrium: fermionic representation

The electrical current through an arbitrary junction connecting quantum wires of spinless interacting fermions is calculated in fermionic representation. The wires are adiabatically attached to two reservoirs at chemical potentials differing by the applied voltage bias. The relevant scale-dependent contributions in perturbation theory in the interaction up to infinite order are evaluated and summed up. The result allows one to construct renormalization group equations for the conductance as a function of voltage (or temperature, wire length). There are two fixed points at which the conductance follows a power law in terms of a scaling variable $Λ$, which equals the bias voltage $V$, if $V$ is the largest energy scale compared to temperature $T$ and inverse wire length $L^{-1}$, and interpolates between these quantities in the crossover regimes.

cond-mat.str-el↗

arXiv2013

Chiral Y-junction of Luttinger liquid wires at strong coupling: fermionic representation

We calculate the conductances of a three-terminal junction set-up of spinless Luttinger liquid wires threaded by a magnetic flux, allowing for different interaction strength g_3 != g in the third wire. We employ the fermionic representation in the scattering state picture, allowing for a direct calculation of the linear response conductances, without the need of introducing contact resistances at the connection points to the outer ideal leads. The matrix of conductances is parametrized by three variables. For these we derive coupled renormalization group (RG) equations, by summing up infinite classes of contributions in perturbation theory. The resulting general structure of the RG equations may be employed to describe junctions with an arbitrary number of wires and arbitrary interaction strength in each wire. The fixed point structure of these equations (for the chiral Y-junction) is analyzed in detail. For repulsive interaction (g,g_3>0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g<0 and/or g_3<0) four fixed points are found, the stability of which depends on the interaction strength. We confirm our previous weak-coupling result of lines of fixed points for special values of the interaction parameters reaching into the strong coupling domain. We find new fixed points not discussed before, even at the symmetric line g=g_3, at variance with the results of Oshikawa et al. The pair tunneling phenomenon conjectured by the latter authors is not found by us.

cond-mat.str-el↗

arXiv2012

Chiral Y-junction of Luttinger liquid wires at weak coupling: lines of stable fixed points

We study the transport properties of a system of three Luttinger liquid wires (with different interaction strengths g, g_3), connected through a Y-junction (main wire and tunneling tip) threaded by magnetic flux, within the scattering state formalism. The scattering matrix and the matrix of conductances are parametrized by three variables. For these we derive coupled RG equations, up to second order in the interaction. The fixed point structure of these equations is analyzed in detail. For repulsive interaction (g, g_3>0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g<0 and/or g_3<0) four fixed points are found, whose stability depends on the interaction strength. For special values of the interaction parameters (a) g=0, g_3<0 or (b) g_3+g^2/2=0 and g<0 we find whole lines of stable fixed points. In certain regions of the g-g_3-plane the RG flow is towards a fixed point without chirality, implying that the effect of the magnetic flux is completely screened.

cond-mat.str-el↗

arXiv2012

Transport through asymmetric two-lead junctions of Luttinger liquid wires

We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g_1, g_2, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g_1, g_2. The regions of stability of the two fixed points corresponding to conductance G=0 and G=1, respectively, are determined.

cond-mat.str-el↗

arXiv2011

Y-junction connecting Luttinger liquids: fixed point structure and conductances

We study the transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra language and focus on the case of a symmetric set-up, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, first in a ladder summation up to infinite order in the interaction. The fixed point structure and the implicit solution of these equations is presented. It is shown that higher order terms beyond the ladder approximation do not change the scaling behavior near the fixed points. For sufficiently strong attractive interaction a new fixed point with unusual properties is found.

cond-mat.str-el↗

arXiv2011

Constraints on conductances for Y-junction of quantum wires

We consider the Y-junction, connecting three quantum wires, in the scattering states formalism. In the absence of fermionic interaction we analyze the restrictions on the values of conductance matrix, imposed by the unitarity of scattering S-matrix. Using the combination of numerical and analytical results, we describe the four-dimensional body of values of reduced conductance matrix. We show that this body touches the unit sphere at six points only, in accordance with Birkhoff-von Neumann theorem. It implies that the Abelian bosonization analysis for the vanishing interaction strength can be performed only in the vicinity of these six points.

cond-mat.str-el↗