Dirac materials have unique transport properties, partly due to the presence of surface states. A... more 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-onedimensional 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.
We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum... more 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.
We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) inter... more 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 = 0, 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.
The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is ... more 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.
We discuss transport through an interferometer formed by helical edge states of the quantum spin ... more 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%.
We study the transport properties of three Luttinger liquid wires (with possibly different intera... more 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.
We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond ... more We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.
We study the transport properties of three Luttinger liquid wires (with possibly different intera... more 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. I.
Journal of Experimental and Theoretical Physics Letters, 1999
The Landau quantization for the electron gas on the surface of a sphere is considered. It is show... more The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong fields the lowest energy states are those with magnetic quantum numbers m of order of ⌽/⌽ 0 , the number of magnetic flux quanta piercing the sphere. For an electron gas of low density ͑semiconducting situation͒ it leads to the formation of an electronic stripe on the equator of the sphere in high fields.
We study the optical response of a strongly correlated electron system near the metal-insulator t... more We study the optical response of a strongly correlated electron system near the metal-insulator transition using a mapping to the sine-Gordon model. With semiclassical quantization, the spectral weight is distributed between a Drude peak and absorption lines due to breathers. We calculate the Drude weight, the optical gap, and the lineshape of breather absorption.
We study four-lead junction of semi-infinite wires by using fermionic representation in the scatt... more 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.
We study the spin fluctuations of the oxygen deficient planes of YBa2Cu3O6+x. The Cu-O chains tha... more We study the spin fluctuations of the oxygen deficient planes of YBa2Cu3O6+x. The Cu-O chains that constitute these planes are described by a model that includes antiferromagnetic interactions between spins and Kondo-like scattering of oxygen holes. The spectrum of magnetic excitations shows the presence of incommensurate dynamic fluctuations along the direction of the chains. The presence of itinerant holes is responsible for the existence of important differences between the spin dynamics of this system and that of a quasi-one-dimensional localized antiferromagnet. We comment on the possibility of experimental observation of these fluctuations.
We calculate the conductances of a Y-junction setup of Luttinger liquid wires threaded by a magne... more We calculate the conductances of a Y-junction setup of Luttinger liquid wires threaded by a magnetic flux, allowing for different interaction strength g3 = g in the third wire. 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, within the scattering state formalism. The fixed point structure of these equations is analyzed in detail. For repulsive interaction (g, g3 > 0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g < 0 and/or g3 < 0) four fixed points are found, whose stability depends on the interaction strength. For special values of the interaction parameters (a) g = 0, g3 < 0 or (b) g3 + g 2 /2 = 0 and g < 0 we find whole lines of stable fixed points. We conjecture that lines of fixed points appear generically at interfaces in interaction coupling constant space separating two regions with different stable fixed points. We also find that in certain regions of the g-g3-plane the RG flow is towards a fixed point without chirality, implying that the effect of the magnetic flux is completely screened.
We consider an electron gas moving on the surface of a sphere in a uniform magnetic field. An exa... more We consider an electron gas moving on the surface of a sphere in a uniform magnetic field. An exact solution of the problem is found in terms of oblate spheroidal functions, depending on the parameter p=Phi/Phi0, the number of flux quanta piercing the sphere. The regimes of weak and strong fields are discussed, and the Green's functions are found for both limiting cases in closed form. In weak fields the magnetic susceptibility reveals a set of jumps at half-integer p. The strong-field regime is characterized by the formation of Landau levels and localization of the electron states near the poles of the sphere defined by a direction of the field. The effects of coherence within the sphere are lost when its radius exceeds the mean free path.
... In three dimensions the spatial dependence of this interaction was obtained in Ref. ... 2. Th... more ... In three dimensions the spatial dependence of this interaction was obtained in Ref. ... 2. The Gaussian integration over k gives G i ,R m 2 n/2 e i 1 n/2 0 d n/2 exp ze i 2 e i 7 mR 2 . We notice that the last integral can be exwith pressed via the modified Bessel Mcdonald function,3 ...
We consider the correlation functions in a gas of electrons moving within a thin layer on the sur... more We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect exchange, superconducting Cooper loop and ``density-density'' correlation function is obtained. The systematic comparison with planar results is made, the effects of spherical geometry are outlined. The quantum coherence of electrons leads to the enhancement of all correlations for the points-antipodes on the sphere. This effect is lost when the radius of the sphere exceeds the temperature coherence length.
ABSTRACT The optical conductivity of a d-CDW conductor is calculated for electrons on a square la... more ABSTRACT The optical conductivity of a d-CDW conductor is calculated for electrons on a square lattice and a nearest-neighbor charge-charge interaction using the lowest-order conserving approximation. The spectral properties of the Drude-like peak at low frequencies and the broad hump due to transitions across the gap at large frequencies are discussed, also as a function of temperature and of the second-nearest neighbor hopping term t&#39;. We find that vertex corrections enhance the d.c. conductivity, make the Drude peak narrower and provide a smooth transition from a renormalized regime at low to the bare theory at high frequencies. It is also shown that vertex corrections enhance the temperature dependence of the restricted optical sum leading to a non-negligible violation of the sum rule in the d-CDW state.
ABSTRACT Charge density waves with unconventional order parameters, for instance, with d-wave sym... more ABSTRACT Charge density waves with unconventional order parameters, for instance, with d-wave symmetry (DDW), may be relevant in the underdoped regime of high-T_c cuprates or other quasi-one or two dimensional metals. A DDW state is characterized by two branches of low-lying electronic excitations. The resulting quantum mechanical current has an inter-branch component which leads to an additional mass term in the expression for the Hall conductivity. This extra mass term is parametrically enhanced near the ``hot spots&#39;&#39; of fermionic dispersion and is non-neglegible as is shown by numerical calculations of the Hall number in the DDW state.
Dirac materials have unique transport properties, partly due to the presence of surface states. A... more 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-onedimensional 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.
We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum... more 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.
We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) inter... more 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 = 0, 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.
The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is ... more 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.
We discuss transport through an interferometer formed by helical edge states of the quantum spin ... more 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%.
We study the transport properties of three Luttinger liquid wires (with possibly different intera... more 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.
We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond ... more We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.
We study the transport properties of three Luttinger liquid wires (with possibly different intera... more 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. I.
Journal of Experimental and Theoretical Physics Letters, 1999
The Landau quantization for the electron gas on the surface of a sphere is considered. It is show... more The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong fields the lowest energy states are those with magnetic quantum numbers m of order of ⌽/⌽ 0 , the number of magnetic flux quanta piercing the sphere. For an electron gas of low density ͑semiconducting situation͒ it leads to the formation of an electronic stripe on the equator of the sphere in high fields.
We study the optical response of a strongly correlated electron system near the metal-insulator t... more We study the optical response of a strongly correlated electron system near the metal-insulator transition using a mapping to the sine-Gordon model. With semiclassical quantization, the spectral weight is distributed between a Drude peak and absorption lines due to breathers. We calculate the Drude weight, the optical gap, and the lineshape of breather absorption.
We study four-lead junction of semi-infinite wires by using fermionic representation in the scatt... more 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.
We study the spin fluctuations of the oxygen deficient planes of YBa2Cu3O6+x. The Cu-O chains tha... more We study the spin fluctuations of the oxygen deficient planes of YBa2Cu3O6+x. The Cu-O chains that constitute these planes are described by a model that includes antiferromagnetic interactions between spins and Kondo-like scattering of oxygen holes. The spectrum of magnetic excitations shows the presence of incommensurate dynamic fluctuations along the direction of the chains. The presence of itinerant holes is responsible for the existence of important differences between the spin dynamics of this system and that of a quasi-one-dimensional localized antiferromagnet. We comment on the possibility of experimental observation of these fluctuations.
We calculate the conductances of a Y-junction setup of Luttinger liquid wires threaded by a magne... more We calculate the conductances of a Y-junction setup of Luttinger liquid wires threaded by a magnetic flux, allowing for different interaction strength g3 = g in the third wire. 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, within the scattering state formalism. The fixed point structure of these equations is analyzed in detail. For repulsive interaction (g, g3 > 0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g < 0 and/or g3 < 0) four fixed points are found, whose stability depends on the interaction strength. For special values of the interaction parameters (a) g = 0, g3 < 0 or (b) g3 + g 2 /2 = 0 and g < 0 we find whole lines of stable fixed points. We conjecture that lines of fixed points appear generically at interfaces in interaction coupling constant space separating two regions with different stable fixed points. We also find that in certain regions of the g-g3-plane the RG flow is towards a fixed point without chirality, implying that the effect of the magnetic flux is completely screened.
We consider an electron gas moving on the surface of a sphere in a uniform magnetic field. An exa... more We consider an electron gas moving on the surface of a sphere in a uniform magnetic field. An exact solution of the problem is found in terms of oblate spheroidal functions, depending on the parameter p=Phi/Phi0, the number of flux quanta piercing the sphere. The regimes of weak and strong fields are discussed, and the Green's functions are found for both limiting cases in closed form. In weak fields the magnetic susceptibility reveals a set of jumps at half-integer p. The strong-field regime is characterized by the formation of Landau levels and localization of the electron states near the poles of the sphere defined by a direction of the field. The effects of coherence within the sphere are lost when its radius exceeds the mean free path.
... In three dimensions the spatial dependence of this interaction was obtained in Ref. ... 2. Th... more ... In three dimensions the spatial dependence of this interaction was obtained in Ref. ... 2. The Gaussian integration over k gives G i ,R m 2 n/2 e i 1 n/2 0 d n/2 exp ze i 2 e i 7 mR 2 . We notice that the last integral can be exwith pressed via the modified Bessel Mcdonald function,3 ...
We consider the correlation functions in a gas of electrons moving within a thin layer on the sur... more We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect exchange, superconducting Cooper loop and ``density-density'' correlation function is obtained. The systematic comparison with planar results is made, the effects of spherical geometry are outlined. The quantum coherence of electrons leads to the enhancement of all correlations for the points-antipodes on the sphere. This effect is lost when the radius of the sphere exceeds the temperature coherence length.
ABSTRACT The optical conductivity of a d-CDW conductor is calculated for electrons on a square la... more ABSTRACT The optical conductivity of a d-CDW conductor is calculated for electrons on a square lattice and a nearest-neighbor charge-charge interaction using the lowest-order conserving approximation. The spectral properties of the Drude-like peak at low frequencies and the broad hump due to transitions across the gap at large frequencies are discussed, also as a function of temperature and of the second-nearest neighbor hopping term t&#39;. We find that vertex corrections enhance the d.c. conductivity, make the Drude peak narrower and provide a smooth transition from a renormalized regime at low to the bare theory at high frequencies. It is also shown that vertex corrections enhance the temperature dependence of the restricted optical sum leading to a non-negligible violation of the sum rule in the d-CDW state.
ABSTRACT Charge density waves with unconventional order parameters, for instance, with d-wave sym... more ABSTRACT Charge density waves with unconventional order parameters, for instance, with d-wave symmetry (DDW), may be relevant in the underdoped regime of high-T_c cuprates or other quasi-one or two dimensional metals. A DDW state is characterized by two branches of low-lying electronic excitations. The resulting quantum mechanical current has an inter-branch component which leads to an additional mass term in the expression for the Hall conductivity. This extra mass term is parametrically enhanced near the ``hot spots&#39;&#39; of fermionic dispersion and is non-neglegible as is shown by numerical calculations of the Hall number in the DDW state.
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Papers by D. Aristov