Alexander Zyuzin

We theoretically study the coupling of electric charge and spin polarization in an equilibrium and nonequilibrium electric transport across a two dimensional Josephson configuration comprised of disordered surface channels of a three dimensional topological insulator. In the equilibriun state of the system we predict the Edelstein effect, which is much more pronounced than its counterpart in conventional spin orbit coupled materials. Employing a quasiclassical Keldysh technique, we demonstrate that the ground state of system can be experimentally shifted into arbitrary macroscopic superconducting phase differences other than the standard "0" or "pi", constituting a \phi_0-junction, solely by modulating a quasiparticle flow injection into the junction. We propose a feasible experiment where the quasiparticles are injected into the topological insulator surface by means of a normal electrode and voltage gradient so that oppositely oriented stationary spin densities can be developed along the interfaces and allow for directly making use of the spin-momentum locking nature of Dirac fermions in the surface channels. The \phi_0-state is proportional to the voltage difference applied between the injector electrode and superconducting terminals that calibrates the injection rate of particles and, therefore, the \phi_0 shift.

We present a theory of the anomalous Hall effect in a topological Weyl superconductor with broken time reversal symmetry. Specifically, we consider a ferromagnetic Weyl metal with two Weyl nodes of opposite chirality near the Fermi energy. In the presence of inversion symmetry, such a metal experiences a weak-coupling Bardeen-Cooper-Schrieffer (BCS) instability, with pairing of parity-related eigenstates. Due to the nonzero topological charge, carried by the Weyl nodes, such a superconductor is necessarily topologically nontrivial, with Majorana surface states coexisting with the Fermi arcs of the normal Weyl metal. We demonstrate that, surprisingly, the anomalous Hall conductivity of such a superconducting Weyl metal coincides with that of a nonsuperconducting one, under certain conditions, in spite of the nonconservation of charge in a superconductor. We relate this to the existence of an extra (nearly) conserved quantity in a Weyl metal, the chiral charge.

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.

We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation period of helical magnetization is larger than the junction width, we find supercurrent 0-{\pi} crossovers as a function of junction thickness, magnetization strength, and parameters inherent to the helical modulation and surface states. The supercurrent reversals are associated with proximity induced vortices, nucleated along the junction width, where the number of vortices and their locations can be manipulated by means of the superconducting phase difference and the parameters mentioned above.

We theoretically demonstrate that a supercurrent across a two-dimensional topological insulator subjected to an external magnetic field unambiguously reveals the existence of edge-mode superconductivity. When the edge states of a narrow two-dimensional topological insulator are hybridized, an external magnetic field can close the hybridization gap, thus driving a quantum phase transition from insulator to semimetal states of the topological insulator. Importantly, we find a sign reversal of the supercurrent at the quantum phase transition which offers a simple and experimentally feasible way to observe intrinsic properties of topological insulators including edge-mode superconductivity.

The fermionic energy spectrum on the surface of the multilayer honeycomb lattice with rhombohedral stacking has topologically protected flat bands. It is shown that topological phase transition occurs in the anisotropic multilayer graphene-like structure with strongly anisotropic intra-layer coupling, at which two flat bands with opposite chirality merge into one and split, opening up a gap in the energy spectrum, depending on the anisotropy of the intralayer hopping. The dispersion of the flat bands of the multilayer is anisotropic and the density of states is more singular in the vicinity of the transition.

We study two microscopic models of topological insulators in contact with an s-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of scalar and of randomly oriented spin impurities. Here, we require that spin-flip tunneling dominates over spin-conserving one. In the second model the tunnel coupling is realized by an array of single-level quantum dots with randomly oriented spins. It is shown that the tunnel region forms a π-junction where the effective order parameter changes sign. Interestingly, due to the random spin orientation the effective descriptions of both models exhibit time-reversal symmetry. We then discuss how the proposed π-junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates.

We report on a study of intrinsic superconductivity in a Weyl metal, i.e. a doped Weyl semimetal. Two distinct superconducting states are possible in this system in principle: a zero-momentum pairing BCS state, with point nodes in the gap function; and a finite-momentum FFLO-like state, with a full nodeless gap. We find that, in an inversion-symmetric Weyl metal the odd-parity BCS state has a lower energy than the FFLO state, despite the nodes in the gap. The FFLO state, on the other hand, may have a lower energy in a noncentrosymmetric Weyl metal, in which Weyl nodes of opposite chirality have different energy. However, realizing the FFLO state is in general very difficult since the paired states are not related by any exact symmetry, which precludes a weak-coupling superconducting instability. We also discuss some of the physical properties of the nodal BCS state, in particular Majorana and Fermi arc surface states.

We study the effect of bias voltage on the nuclear spin polarization of a ballistic wire, which contains electrons and nuclei interacting via hyperfine interaction. In equilibrium, the localized nuclear spins are helically polarized due to the electron-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Focusing here on non-equilibrium, we find that an applied bias voltage induces a uniform polarization, from both helically polarized and unpolarized spins available for spin flips. Once a macroscopic uniform polarization in the nuclei is established, the nuclear spin helix rotates with frequency proportional to the uniform polarization. The uniform nuclear spin polarization monotonically increases as a function of both voltage and temperature, reflecting a thermal activation behavior. Our predictions offer specific ways to test experimentally the presence of a nuclear spin helix polarization in semiconducting quantum wires.

We show that Weyl semimetals with broken time-reversal symmetry can host chiral electromagnetic waves. The magnetization that results in a momentum space separation of a pair of opposite chirality Weyl nodes is also responsible for the non-zero gyration vector in the system. It is then shown that chiral electromagnetic wave can propagate in a region of space where the gyration vector flips its direction. Such waves are analogs of quantum Hall edge states for photons.

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities on the surface of a three-dimensional topological insulator with proximity induced superconductivity. A superconductor placed on the top of the topological insulator induces a gap in the surface electron states and gives rise to a long-range in-plane antiferromagnetic RKKY interaction. This interaction is frustrated due to strong spin-orbit coupling, inversely proportional to the distance between magnetic impurities if the distance between magnetic impurities is smaller than the superconducting coherence length, and dominates over the ferromagnetic and Dzialoshinskii-Moriya type interactions if the distance between magnetic impurities is larger than the superconducting coherence length. The condition for the subgap states that are bound to the magnetic impurities is found.

We study the nuclear spin relaxation in a ballistic nanowire with hyperfine and Rashba spin-orbit interactions (SOI) and in the presence of magnetic field and electron interactions. The relaxation rate shows pronounced peaks as function of magnetic field and chemical potential due to van Hove singularities in the Rashba bands. As a result, the regimes of weak and strong SOIs can be distinguished by the number of peaks in the rate. The relaxation rate increases with increasing magnetic field if both Rashba subbands are occupied, whereas it decreases if only the lowest one is occupied.

We consider a model of ballistic quasi-one-dimensional semiconducting wire with intrinsic spin-orbit interaction placed on the surface of a bulk s-wave superconductor (SC), in the presence of an external magnetic field. This setup has been shown to give rise to a topological superconducting state in the wire, characterized by a pair of Majorana-fermion (MF) bound states formed at the two ends of the wire. Here, we demonstrate that besides the well-known direct-overlap-induced energy splitting, the two MF bound states may hybridize via elastic tunneling processes through virtual quasiparticle states in the SC, giving rise to an additional energy splitting between MF states from the same as well as from different wires.

We consider the effect of electron-electron interaction on the density of states of a disordered paramagnetic conductor in the presence of spin accumulation and magnetic field. We show that interaction correction to electron density of states of the paramagnet may exhibit singularities at energies corresponding to the difference between chemical potentials of electrons with opposite spins. We also discuss correlation effects on conductivity in metallic as well as in hopping regimes.

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a $\theta$-term in the action for the electromagnetic field, where $\theta$ is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that, somewhat surprisingly, the $\theta$-term and the corresponding topological response are insensitive to translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes.

Weyl semimetal is a new topological state of matter, characterized by the presence of nondegenerate band-touching nodes, separated in momentum space, in its bandstructure. Here we discuss a particular realization of a Weyl semimetal: a superlattice heterostructure, made of alternating layers of topological insulator (TI) and normal insulator (NI) material, introduced by one of us before. The Weyl node splitting is achieved most easily in this system by breaking time-reversal (TR) symmetry, for example by magnetic doping. If, however, spatial inversion (I) symmetry remains, the Weyl nodes will occur at the same energy, making it possible to align the Fermi energy simultaneously with both nodes. The goal of this work is to explore the consequences of breaking the I symmetry in this system. We demonstrate that, while this generally moves the Weyl nodes to different energies, thus eliminating nodal semimetal and producing a state with electron and hole Fermi surfaces, the topological properties of the Weyl semimetal state, i.e. the chiral edge states and the corresponding Hall conductivity, survive for moderate I symmetry breaking. Moreover, we demonstrate that a new topological phenomenon arises in this case, if an external magnetic field along the growth direction of the heterostructure is applied. Namely, this leads to an equilibrium dissipationless current, flowing along the direction of the field, whose magnitude is proportional to the energy difference between the Weyl nodes and to the magnetic field, with a universal coefficient, given by a combination of fundamental constants.

We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau level spectrum of the film as a function of the applied magnetic field and the magnitude of the hybridization matrix element, taking into account both the orbital and the Zeeman spin splitting effects of the field. For an undoped film, we find a quantum phase transition between a state with a zero Hall conductivity and a state with a quantized Hall conductivity equal to $e^2/h$, as a function of the magnitude of the applied field. The transition is driven by the competition between the Zeeman and the hybridization energies.

It is well-known that helical surface states of a three-dimensional topological insulator (TI) do not respond to a static in-plane magnetic field. Formally this occurs because the in-plane magnetic field appears as a vector potential in the Dirac Hamiltonian of the surface states and can thus be removed by a gauge transformation of the surface electron wavefunctions. Here we show that when the top and bottom surfaces of a thin film of TI are hybridized and the Fermi level is in the hybridization gap, a nonzero diamagnetic response appears. Moreover, a quantum phase transition occurs at a finite critical value of the parallel field from an insulator with a diamagnetic response to a semimetal with a vanishing response to the parallel field.

We consider a metamagnetic phase transition of itinerant electrons in the metamagnetic- ferromagnetic metal junction. The current flow between a ferromagnetic metal and a metamagnetic metal produces the non-equilibrium spin imbalance acting as an effective magnetic field and initiating the first-order type transition from low- to high-magnetization states of the metamagnet in the vicinity of the ferromagnet. We show that the current dependence of the length of high-magnetization state region diverges at some threshold value, due to nonequilibrium shift, generated in a contact between the high and low magnetization states of the metamagnetic metal.

We study metamagnetic phase transition of itinerant electrons controlled by the spin-injection mechanism. The current flow between a ferromagnetic metal and a metamagnetic metal produces the nonequilibrium shift of chemical potential for spin-up and spin-down electrons. This shift acts as an effective magnetic field driving the metamagnetic transition between low and high magnetization states of the metamagnet in the vicinity to the contact with the ferromagnet. We show that high magnetization state of the metamagnet self propels into the bulk of the metamagnet and the length of this state has threshold dependence on the electrical current.

We theoretically study the effect of exchange interaction on the non-equilibrium spin waves in disordered paramagnetic metals under the spin injection condition. We show that the gapless spectrum of spin waves, describing the spin precession in the absence of the applied magnetic field, changes sign to negative on the paramagnetic side near the ferromagnet-paramagnet phase transition. The damping of spin waves is small in the limit when electron-electron exchange energy is larger than the inverse electron mean free time, while in the opposite limit the propagation of spin waves is strongly suppressed. We discuss the amplification of the electromagnetic field by the non-equilibrium spin waves.

We consider Aharonov-Bohm (AB) effect at normal-metal-inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superconducting state transition. It is shown that magnetic flux can increase the transition temperature and AB oscillations can have the double-peak structure at one period. Expressions for fluctuational heat capacity and persistent current are calculated for a thin ring and a cylinder. We also discuss the effect of fluctuations interaction in the nonuniform states in the vicinity of the superconducting transition.

We study AB oscillations of transition temperature, paraconductivity and specific heat of thin ring in the regime of inhomogeneous Larkin- Ovchinnikov- Fulde- Ferrell (LOFF) superconducting state. We found that in contrast to uniform superconductivity magnetic flux might increase the critical temperature of LOFF state. Degeneracy of the inhomogeneous superconducting state reveals in double peak structure of AB oscillations.

It is shown that, in an edge superconducting layer of a thin film in a magnetic field perpendicular to the film plane, phase slip centers are formed. The centers arise below the superconducting transition temperature because of the thermal fluctuations of the order parameter and lead to the suppression of superconductivity. The resistance corresponding to such fluctuations is determined, and the contribution of the Aslamazov-Larkin correction to the conductivity of a thin film in magnetic fields slightly exceeding the critical field that breaks the surface superconductivity is calculated.

The conductance of a point contact between two hopping insulators is expected to be dominated by the individual localized states in its vicinity. Here, we study the additional effects due to an external magnetic field. Combined with the measured conductance, the measured magnetoresistance provides detailed information on these states (e.g., their localization length, the energy difference, and the hopping distance between them). We also calculate the statistics of this magnetoresistance, which can be collected by changing the gate voltage in a single device. Since the conductance is dominated by the quantum interference of particular mesoscopic structures near the point contact, it is predicted to exhibit Aharonov-Bohm oscillations, which yield information on the geometry of these structures. These oscillations also depend on local spin accumulation and correlations, which can be modified by the external field. Finally, we also estimate the mesoscopic Hall voltage due to these structures.

We develop a theory of the low-temperature charge transfer between a superconductor and a hopping insulator. We show that the charge transfer is governed by the coherent two-electron -- Cooper pair conversion process, time reversal reflection, where electrons tunnel into superconductor from the localized states in the hopping insulator located near the interface, and calculate the corresponding interface resistance. This process is an analog to conventional Andreev reflection process. We show that the time reversal interface resistance is accessible experimentally, and that in mesoscopic structures it can exceed the bulk hopping resistance.

Experimental and theoretical studies on transport in semiconductor samples with superconducting electrodes are reported. We focus on the samples close to metal-insulator transition. In metallic samples, a peak of negative magnetoresistance at fields lower than critical magnetic field of the leads was observed. This peak is attributed to restoration of a single-particle tunneling emerging with suppression of superconductivity. The experimental results allow us to estimate tunneling transparency of the boundary between superconductor and metal. In contrast, for the insulating samples no such a peak was observed. We explain this behavior as related to properties of transport through the contact between superconductor and hopping conductor. This effect can be used to discriminate between weak localization and strong localization regimes.

Hopping transport through a point contact between two bulk semiconductors is considered for the case when the contact size is much smaller than a typical hopping length in the bulk. In this case the conductance is controlled by a single hop between the two sites located the opposite banks of the contact. For the variable range hopping (VRH) the choice of the pair depends on temperature, and the temperature dependence of the conductance exhibits exponentially large mesoscopic fluctuations. For large enough voltage the conductance is strongly nonlinear and also exhibits giant fluctuations as a result of “switching” between different “critical pairs.” It also exhibits regions of negative differential resistance due to resonant tunneling effective at some “resonant” values of the bias. At higher biases the nonlinear I(V) curve tends to a smooth one (I∝V2). A comparison to existing theoretical and experimental works relevant to the problem is made.

The hopping transport through the point contact between two semiconductors is considered for the case when the conductance is controlled by a single hop through the constriction. The choice of the critical pair of the hopping sites depends on temperature, and the temperature dependence of the conductance exhibits exponentially large mesoscopic fluctuations. For large biases the conductance is strongly nonlinear and also exhibits giant fluctuations as a result of switching between different critical pairs. The contribution of each of such pairs to the I-V curve has a step-like form with a region of negative differential resistance related to resonant tunneling which appears to be effective at some resonant values of the bias.