Alexey Kovalev - Academia.edu (original) (raw)
Papers by Alexey Kovalev
Physical Review Research, 2020
We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. W... more We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general non-conserved, but for certain symmetries and spin polarizations the averaged effect of non-conserving terms can vanish. We formulate a general linear response theory for magnons in noncollinear antiferromagnets subject to a temperature gradient and analyze the effect of symmetries on the response tensor. We apply this theory to single-layer potassium iron jarosite KFe3(OH)6(SO4)2 and predict a measurable spin current response.
Journal of Applied Physics
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana ferm... more The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmion...
We propose the manipulation of Majorana edge states via hybridization and spin currents in a nano... more We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle – an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin–orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques
The techniques of distance verification known for general linear codes are re-applied to quantum ... more The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks’ sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes. Index Terms – Distance verification, complexity bounds, quantum stabilizer codes, LDPC codes, erasure correction
Physical Review Letters, 2020
We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose ... more We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.
Physical Review B, 2020
We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromag... more We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analogue of the inverse spin-galvanic effect of electrons. We derive a linear response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., KFe3(OH)6(SO4)2, and a noncollinear breathing pyrochlore antiferromagnet, e.g., LiGaCr4O8. The shapes of our numerically evaluated response tensors agree with those implied by the magnetic symmetry. Assuming a realistic temperature gradient of 10 K/mm, we find two-dimensional spin densities of up to ∼ 10 6 /cm 2 and three-dimensional bulk spin densities of up to ∼ 10 14 /cm 3 , encouraging an experimental detection.
Physical Review B, 2019
Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves ... more Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves the topological electronic states coupled to the AFM order parameter known as the Néel vector. The control of these states is envisioned through manipulation of the Néel vector by spin-orbit torques driven by electric currents. Here we propose a different approach favorable for low-power AFM spintronics, where the control of the topological states in a two-dimensional material, such as graphene, is performed via the proximity effect by the voltage induced switching of the Néel vector in an adjacent magnetoelectric AFM insulator, such as chromia. Mediated by the symmetry protected boundary magnetization and the induced Rashba-type spin-orbit coupling at the interface between graphene and chromia, the emergent topological phases in graphene can be controlled by the Néel vector. Using density functional theory and tightbinding Hamiltonian approaches, we model a graphene/Cr2O3 (0001) interface and demonstrate non-trivial band gap openings in the graphene Dirac bands asymmetric between the K and K′ valleys. This gives rise to an unconventional quantum anomalous Hall effect (QAHE) with a quantized value of 2e 2 /h and an additional step-like feature at a value close to e 2 /2h, and the emergence of the spin-polarized valley Hall effect (VHE). Furthermore, depending on the Néel vector orientation, we predict the appearance and transformation of different topological phases in graphene across the 180° AFM domain wall, involving the QAHE, the valley-polarized QAHE and the quantum VHE (QVHE), and the emergence of the chiral edge state along the domain wall. These topological properties are controlled by voltage through magnetoelectric switching of the AFM insulator with no need for spin-orbit torques.
Journal of Mathematical Physics, 2019
We consider pairs of few-body Ising models where each spin enters a bounded number of interaction... more We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other after freezing k spins on large-degree sites. Such a pair of Ising models can be interpreted as a two-chain complex with k being the rank of the first homology group. Our focus is on the case where k is extensive, that is, scales linearly with the number of bonds n. Flipping any of these additional spins introduces a homologically nontrivial defect (generalized domain wall). In the presence of bond disorder, we prove the existence of a low-temperature weak-disorder region where additional summation over the defects has no effect on the free energy density f (T) in the thermodynamical limit, and of a high-temperature region where an extensive homological defect does not affect f (T). We also discuss the convergence of the high-and low-temperature series for the free energy density, prove the analyticity of limiting f (T) at high and low temperatures, and construct inequalities for the critical point(s) where analyticity is lost. As an application, we prove multiplicity of the conventionally defined critical points for Ising models on all {f, d} tilings of the infinite hyperbolic plane, where df /(d + f) > 2. Namely, for these infinite graphs, we show that critical temperatures with free and wired boundary conditions differ, T (f) c < T (w) c .
Physical Review A, 2018
We study analytically and numerically decoding properties of finite rate hypergraph-product quant... more We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3, 4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models, and a minimum weight decoding threshold of approximately 7%.
Physical Review B, 2018
We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topolog... more We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters the system can be tuned between the chiral topological insulator (mcTI), three dimensional magnon anomalous Hall (3D-mAH), and Weyl magnon phases.
Physical Review B, 2018
We show that elongated magnetic skyrmions can host Majorana bound states in a proximitycoupled tw... more We show that elongated magnetic skyrmions can host Majorana bound states in a proximitycoupled two-dimensional electron gas sandwiched between a chiral magnet and an s-wave superconductor. Our proposal requires stable skyrmions with unit topological charge, which can be realized in a wide range of multilayer magnets, and allows quantum information transfer by using standard methods in spintronics via skyrmion motion. We also show how braiding operations can be realized in our proposal.
Physical Review Materials, 2018
We formulate and study the general boundary conditions dictating the magnetization profile in the... more We formulate and study the general boundary conditions dictating the magnetization profile in the vicinity of an interface between magnets with dissimilar properties. Boundary twists in the vicinity of an edge due to Dzyaloshinskii-Moriya interactions have been first discussed in [Wilson et al., Phys. Rev. B 88, 214420 (2013)] and in [Rohart and Thiaville, Phys. Rev. B 88, 184422 (2013)]. We show that in general case the boundary conditions lead to the magnetization profile corresponding to the Néel, Bloch, or intermediate twist. We explore how such twists can be utilized for creation of skyrmions and antiskyrmions, e.g., in a view of magnetic memory applications. To this end, we study various scenarios how skyrmions and antiskyrmions can be created from interface magnetization twists due to local instabilities. We also show that a judicious choice of Dzyaloshinskii-Moriya tensor (hence a carefully designed material) can lead to local instabilities generating certain types of skyrmions or antiskyrmions. The local instabilities are shown to appear in solutions of the Bogoliubov-de-Gennes equations describing ellipticity of magnon modes bound to interfaces. In one considered scenario, a skyrmion-antiskyrmion pair can be created due to instabilities at an interface between materials with properly engineered Dzyaloshinskii-Moriya interactions. We use micromagnetics simulations to confirm our analytical predictions.
Physical Review B, 2017
Spin-orbit coupling effects occurring in non-centrosymmetric materials are known to be responsibl... more Spin-orbit coupling effects occurring in non-centrosymmetric materials are known to be responsible for non-trivial spin configurations and a number of emergent physical phenomena. Ferroelectric materials may be especially interesting in this regard due to reversible spontaneous polarization making possible for a non-volatile electrical control of the spin degrees of freedom. Here, we explore a technologically relevant oxide material, HfO 2 , which has been shown to exhibit robust ferroelectricity in a non-centrosymmetric orthorhombic phase. Using theoretical modelling based on density-functional theory, we investigate the spin-dependent electronic structure of the ferroelectric HfO 2 and demonstrate the appearance of chiral spin textures driven by spin-orbit coupling. We analyze these spin configurations in terms of the Rashba and Dresselhaus effects within the ⋅ k p Hamiltonian model and find that the Rashba-type spin texture dominates around the valence band maximum, while the Dresselhaus-type spin texture prevails around the conduction band minimum. The latter is characterized by a very large Dresselhaus constant λ D = 0.578 eV Å, which allows using this material as a tunnel barrier to produce tunneling anomalous and spin Hall effects that are reversible by ferroelectric polarization.
IEEE Transactions on Information Theory, 2017
The techniques of distance verification known for general linear codes are reapplied to quantum s... more The techniques of distance verification known for general linear codes are reapplied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks' sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes.
Physical Review Letters, 2016
We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an anti... more We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with non-trivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.
2016 IEEE International Symposium on Information Theory (ISIT), 2016
The problem of finding code distance has been long studied for the generic ensembles of linear co... more The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are known for distance verification in other ensembles of linear codes. Our goal is to redesign the existing generic algorithms of distance verification and derive their complexity for LDPC codes. We obtain new complexity bounds with provable performance expressed in terms of the erasure-correcting thresholds of long LDPC codes. These bounds exponentially reduce complexity estimates known for linear codes.
Physical Review B, 2016
Recently, there has been substantial interest in realizations of skyrmions, in particular in quas... more Recently, there has been substantial interest in realizations of skyrmions, in particular in quasi-2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. We find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.
Physical Review B, 2014
We propose an experiment that would establish the entanglement of Majorana zero modes in semicond... more We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple "keyboard" gating, and projective measurement. Simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.
We suggest several techniques to improve the toric codes and the finite-rate generalized toric co... more We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Zémor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal singlequbit-encoding toric codes with block length n = t 2 +(t+1) 2 and distance d = 2t + 1, t = 1, 2,. . .. We also suggest several related algebraic constructions which increase the rate of the existing hypergraph-product codes by up to four times.
Solid State Communications, 2014
We propose the manipulation of Majorana edge states via hybridization and spin currents in a nano... more We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle-an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin-orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques.
Physical Review Research, 2020
We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. W... more We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general non-conserved, but for certain symmetries and spin polarizations the averaged effect of non-conserving terms can vanish. We formulate a general linear response theory for magnons in noncollinear antiferromagnets subject to a temperature gradient and analyze the effect of symmetries on the response tensor. We apply this theory to single-layer potassium iron jarosite KFe3(OH)6(SO4)2 and predict a measurable spin current response.
Journal of Applied Physics
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana ferm... more The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmion...
We propose the manipulation of Majorana edge states via hybridization and spin currents in a nano... more We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle – an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin–orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques
The techniques of distance verification known for general linear codes are re-applied to quantum ... more The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks’ sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes. Index Terms – Distance verification, complexity bounds, quantum stabilizer codes, LDPC codes, erasure correction
Physical Review Letters, 2020
We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose ... more We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.
Physical Review B, 2020
We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromag... more We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analogue of the inverse spin-galvanic effect of electrons. We derive a linear response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., KFe3(OH)6(SO4)2, and a noncollinear breathing pyrochlore antiferromagnet, e.g., LiGaCr4O8. The shapes of our numerically evaluated response tensors agree with those implied by the magnetic symmetry. Assuming a realistic temperature gradient of 10 K/mm, we find two-dimensional spin densities of up to ∼ 10 6 /cm 2 and three-dimensional bulk spin densities of up to ∼ 10 14 /cm 3 , encouraging an experimental detection.
Physical Review B, 2019
Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves ... more Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves the topological electronic states coupled to the AFM order parameter known as the Néel vector. The control of these states is envisioned through manipulation of the Néel vector by spin-orbit torques driven by electric currents. Here we propose a different approach favorable for low-power AFM spintronics, where the control of the topological states in a two-dimensional material, such as graphene, is performed via the proximity effect by the voltage induced switching of the Néel vector in an adjacent magnetoelectric AFM insulator, such as chromia. Mediated by the symmetry protected boundary magnetization and the induced Rashba-type spin-orbit coupling at the interface between graphene and chromia, the emergent topological phases in graphene can be controlled by the Néel vector. Using density functional theory and tightbinding Hamiltonian approaches, we model a graphene/Cr2O3 (0001) interface and demonstrate non-trivial band gap openings in the graphene Dirac bands asymmetric between the K and K′ valleys. This gives rise to an unconventional quantum anomalous Hall effect (QAHE) with a quantized value of 2e 2 /h and an additional step-like feature at a value close to e 2 /2h, and the emergence of the spin-polarized valley Hall effect (VHE). Furthermore, depending on the Néel vector orientation, we predict the appearance and transformation of different topological phases in graphene across the 180° AFM domain wall, involving the QAHE, the valley-polarized QAHE and the quantum VHE (QVHE), and the emergence of the chiral edge state along the domain wall. These topological properties are controlled by voltage through magnetoelectric switching of the AFM insulator with no need for spin-orbit torques.
Journal of Mathematical Physics, 2019
We consider pairs of few-body Ising models where each spin enters a bounded number of interaction... more We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other after freezing k spins on large-degree sites. Such a pair of Ising models can be interpreted as a two-chain complex with k being the rank of the first homology group. Our focus is on the case where k is extensive, that is, scales linearly with the number of bonds n. Flipping any of these additional spins introduces a homologically nontrivial defect (generalized domain wall). In the presence of bond disorder, we prove the existence of a low-temperature weak-disorder region where additional summation over the defects has no effect on the free energy density f (T) in the thermodynamical limit, and of a high-temperature region where an extensive homological defect does not affect f (T). We also discuss the convergence of the high-and low-temperature series for the free energy density, prove the analyticity of limiting f (T) at high and low temperatures, and construct inequalities for the critical point(s) where analyticity is lost. As an application, we prove multiplicity of the conventionally defined critical points for Ising models on all {f, d} tilings of the infinite hyperbolic plane, where df /(d + f) > 2. Namely, for these infinite graphs, we show that critical temperatures with free and wired boundary conditions differ, T (f) c < T (w) c .
Physical Review A, 2018
We study analytically and numerically decoding properties of finite rate hypergraph-product quant... more We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3, 4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models, and a minimum weight decoding threshold of approximately 7%.
Physical Review B, 2018
We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topolog... more We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters the system can be tuned between the chiral topological insulator (mcTI), three dimensional magnon anomalous Hall (3D-mAH), and Weyl magnon phases.
Physical Review B, 2018
We show that elongated magnetic skyrmions can host Majorana bound states in a proximitycoupled tw... more We show that elongated magnetic skyrmions can host Majorana bound states in a proximitycoupled two-dimensional electron gas sandwiched between a chiral magnet and an s-wave superconductor. Our proposal requires stable skyrmions with unit topological charge, which can be realized in a wide range of multilayer magnets, and allows quantum information transfer by using standard methods in spintronics via skyrmion motion. We also show how braiding operations can be realized in our proposal.
Physical Review Materials, 2018
We formulate and study the general boundary conditions dictating the magnetization profile in the... more We formulate and study the general boundary conditions dictating the magnetization profile in the vicinity of an interface between magnets with dissimilar properties. Boundary twists in the vicinity of an edge due to Dzyaloshinskii-Moriya interactions have been first discussed in [Wilson et al., Phys. Rev. B 88, 214420 (2013)] and in [Rohart and Thiaville, Phys. Rev. B 88, 184422 (2013)]. We show that in general case the boundary conditions lead to the magnetization profile corresponding to the Néel, Bloch, or intermediate twist. We explore how such twists can be utilized for creation of skyrmions and antiskyrmions, e.g., in a view of magnetic memory applications. To this end, we study various scenarios how skyrmions and antiskyrmions can be created from interface magnetization twists due to local instabilities. We also show that a judicious choice of Dzyaloshinskii-Moriya tensor (hence a carefully designed material) can lead to local instabilities generating certain types of skyrmions or antiskyrmions. The local instabilities are shown to appear in solutions of the Bogoliubov-de-Gennes equations describing ellipticity of magnon modes bound to interfaces. In one considered scenario, a skyrmion-antiskyrmion pair can be created due to instabilities at an interface between materials with properly engineered Dzyaloshinskii-Moriya interactions. We use micromagnetics simulations to confirm our analytical predictions.
Physical Review B, 2017
Spin-orbit coupling effects occurring in non-centrosymmetric materials are known to be responsibl... more Spin-orbit coupling effects occurring in non-centrosymmetric materials are known to be responsible for non-trivial spin configurations and a number of emergent physical phenomena. Ferroelectric materials may be especially interesting in this regard due to reversible spontaneous polarization making possible for a non-volatile electrical control of the spin degrees of freedom. Here, we explore a technologically relevant oxide material, HfO 2 , which has been shown to exhibit robust ferroelectricity in a non-centrosymmetric orthorhombic phase. Using theoretical modelling based on density-functional theory, we investigate the spin-dependent electronic structure of the ferroelectric HfO 2 and demonstrate the appearance of chiral spin textures driven by spin-orbit coupling. We analyze these spin configurations in terms of the Rashba and Dresselhaus effects within the ⋅ k p Hamiltonian model and find that the Rashba-type spin texture dominates around the valence band maximum, while the Dresselhaus-type spin texture prevails around the conduction band minimum. The latter is characterized by a very large Dresselhaus constant λ D = 0.578 eV Å, which allows using this material as a tunnel barrier to produce tunneling anomalous and spin Hall effects that are reversible by ferroelectric polarization.
IEEE Transactions on Information Theory, 2017
The techniques of distance verification known for general linear codes are reapplied to quantum s... more The techniques of distance verification known for general linear codes are reapplied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks' sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes.
Physical Review Letters, 2016
We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an anti... more We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with non-trivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.
2016 IEEE International Symposium on Information Theory (ISIT), 2016
The problem of finding code distance has been long studied for the generic ensembles of linear co... more The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are known for distance verification in other ensembles of linear codes. Our goal is to redesign the existing generic algorithms of distance verification and derive their complexity for LDPC codes. We obtain new complexity bounds with provable performance expressed in terms of the erasure-correcting thresholds of long LDPC codes. These bounds exponentially reduce complexity estimates known for linear codes.
Physical Review B, 2016
Recently, there has been substantial interest in realizations of skyrmions, in particular in quas... more Recently, there has been substantial interest in realizations of skyrmions, in particular in quasi-2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. We find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.
Physical Review B, 2014
We propose an experiment that would establish the entanglement of Majorana zero modes in semicond... more We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple "keyboard" gating, and projective measurement. Simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.
We suggest several techniques to improve the toric codes and the finite-rate generalized toric co... more We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Zémor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal singlequbit-encoding toric codes with block length n = t 2 +(t+1) 2 and distance d = 2t + 1, t = 1, 2,. . .. We also suggest several related algebraic constructions which increase the rate of the existing hypergraph-product codes by up to four times.
Solid State Communications, 2014
We propose the manipulation of Majorana edge states via hybridization and spin currents in a nano... more We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle-an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin-orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques.