arXiv subjects

A. V. Rozhkov

Publications and source records attributed to A. V. Rozhkov.

At least 55 records · Page 3Linked to original sources

arXiv2015

Majorana fermions at the edge of superconducting islands

We investigate the properties of electron states localized at the edge of a superconducting island placed on the surface of a topological insulator in a magnetic field. In such systems, Majorana fermions emerge if an odd number of vortices (or odd multivortex vorticity) is hosted by the island; otherwise, no Majorana states exist. Majorana states emerge in pairs: one state is localized near the vortex core, and another at the island edge. We analyze in detail the robustness of Majorana fermions at the edge of the island threaded by a single vortex. If the system parameters are optimized, the energy gap between the Majorana fermion and the first excited state at the edge is of the order of the superconducting gap induced on the surface of the topological insulator. The stability of the Majorana fermion state against a variation of the gate voltage and its sensitivity to the magnetic field allows one to distinguish experimentally the edge Majorana fermion from conventional Dirac fermions.

cond-mat.mes-hall↗

arXiv2015

Electronic spectrum of twisted bilayer graphene

We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range $1^{\circ}\lesssimθ\lesssim30^{\circ}$. We show that at certain angles $θ$ greater than $θ_{c}\approx1.89^{\circ}$ the electronic spectrum acquires a finite gap, whose value could be as large as $80$ meV. However, in an infinitely large and perfectly clean sample the gap as a function of $θ$ behaves non-monotonously, demonstrating exponentially-large jumps for very small variations of $θ$. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment $θ$ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite size $\tilde L$ the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role as $\tilde L$. In the regime of small angles $θ<θ_c$, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of $θ$. The density of states in the metallic phase varies smoothly with $θ$.

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arXiv2014

Generation of localized magnetic moments in the charge-density-wave state

We propose a mechanism explaining the generation of localized magnetic moments in charge-density-wave compounds. Our model Hamiltonian describes an Anderson impurity placed in a host material exhibiting the charge-density wave. There is a region of the model's parameter space, where even weak Coulomb repulsion on the impurity site is able to localize the magnetic moment on the impurity. The phase diagram of a single impurity at T=0 is mapped. To establish the connection with experiment thermodynamic properties of a random impurity ensemble is studied. Magnetic susceptibility of the ensemble diverges at low temperature; heat capacity as a function of the magnetic field demonstrates pronounced low field peak. Both features are consistent with experiments on orthorhombic TaS3 and blue bronze.

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arXiv2014

AA-stacked bilayer graphene in an applied electric field: Tunable antiferromagnetism and coexisting exciton order parameter

We study the electronic properties of AA-stacked bilayer graphene in a transverse electric field. The strong on-site Coulomb repulsion stabilizes the antiferromagnetic order in such a system. The antiferromagnetic order is suppressed by the transverse bias voltage, at least partially. The inter-plane Coulomb repulsion and non-zero voltage stabilize an exciton order parameter. The exciton order parameter coexists with the antiferromagnetism and can be as large as several tens of meV for realistic values of the bias voltage and interaction constants. The application of a transverse bias voltage can be used to control the transport properties of the bilayer.

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arXiv2014

One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior

It is well-known that, generically, the one-dimensional interacting fermions cannot be described in terms of the Fermi liquid. Instead, they present different phenomenology, that of the Tomonaga-Luttinger liquid: the Landau quasiparticles are ill-defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine-tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both the Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both the Tomonaga-Luttinger liquid and the Fermi liquid. Similar to the Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates finite discontinuity at the Fermi energy, which is a hallmark feature of the Fermi liquid. Possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.

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arXiv2014

Tunneling spectrum of a pinned vortex with a robust Majorana state

We study a heterostructure which consists of a topological insulator and a superconductor with a hole. The hole pins a vortex. The system supports a robust Majorana fermion state bound to the vortex core. We investigate the possibility of using scanning tunneling spectroscopy (i) to detect the Majorana fermion in the proposed setup and (ii) to study excited states bound to the vortex core. The Majorana fermion manifests itself as a magnetic-field dependent zero-bias anomaly of the tunneling conductance. Optimal parameters for detecting Majorana fermions have been obtained. In the optimal regime, the Majorana fermion is separated from the excited states by a substantial gap. The number of zero-energy states equals the number of flux quanta in the hole; thus, the strength of the zero-bias anomaly depends on the magnetic field. The lowest energy excitations bound to the core are also studied. The excited states spectrum differs from the spectrum of a typical Abrikosov vortex, providing additional indirect confirmation of the Majorana state observation.

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arXiv2014

Localized electron states near the armchair edge of graphene

It is known that zigzag graphene edge is able to support edge states: there is a non-dispersive single-electron band localized near the zigzag edge. However, it is generally believed that no edge states exist near the armchair edge. In this paper we re-examine this notion. It is demonstrated that while, indeed, the pristine armchair edge does not support any localized states, they do appear if the edge is subjected to suitable modifications (e.g. chemical functionalization). We explicitly present two types of the edge modification which support the localized states. Unlike zigzag edge states, which have zero energy and show no dispersion, properties of the armchair localized states depend sensitively on the type of edge modification. Under suitable conditions they demonstrate pronounced dispersion. While the zigzag edge state wavefunction decays monotonously when we move away from the edge, the armchair edge state wavefunction shows non-monotonous decay. Such states may be observed in scanning tunneling spectroscopy experimentally.

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arXiv2013

Electronic phase separation in iron pnictides

A mechanism for electronic phase separation in iron pnictides is proposed. It is based on the competition between commensurate and incommensurate spin-density-wave phases in a system with an imperfect doping-dependent nesting of a multi-sheeted Fermi surface. We model the Fermi surface by two elliptical electron pockets and three circular hole pockets. The interaction between a charge carrier in a hole band and a carrier in an electron band leads to the formation of spin-density-wave order. The commensurate spin density wave in the parent compound transforms to the incommensurate phase when doping is introduced. We show that, for certain parameter values, the uniform state is unstable with respect to phase separation. The resulting inhomogeneous state consists of regions of commensurate and incommensurate spin-density-wave phases. Our results are in qualitative agreement with recent observations of incommensurate spin density waves and electronic inhomogeneity in iron pnictides.

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arXiv2013

Antiferromagnetic states and phase separation in doped AA-stacked graphene bilayers

We study electronic properties of AA-stacked graphene bilayers. In the single-particle approximation such a system has one electron band and one hole band crossing the Fermi level. If the bilayer is undoped, the Fermi surfaces of these bands coincide. Such a band structure is unstable with respect to a set of spontaneous symmetry violations. Specifically, strong on-site Coulomb repulsion stabilizes antiferromagnetic order. At small doping and low temperatures, the homogeneous phase is unstable, and experiences phase separation into an undoped antiferromagnetic insulator and a metal. The metallic phase can be either antiferromagnetic (commensurate or incommensurate) or paramagnetic depending on the system parameters. We derive the phase diagram of the system on the doping-temperature plane and find that, under certain conditions, the transition from paramagnetic to antiferromagnetic phase may demonstrate re-entrance. When disorder is present, phase separation could manifest itself as a percolative insulator-metal transition driven by doping.

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arXiv2013

Phase separation of antiferromagnetic ground states in systems with imperfect nesting

We analyze the phase diagram for a system of weakly-coupled electrons having an electron- and a hole-band with imperfect nesting. Namely, both bands have spherical Fermi surfaces, but their radii are slightly different, with a mismatch proportional to the doping. Such a model is used to describe: the antiferromagnetism of chromium and its alloys, pnictides, AA-stacked graphene bilayers, as well as other systems. Here we show that the uniform ground state of this model is unstable with respect to electronic phase separation in a wide range of model parameters. Physically, this instability occurs due to the competition between commensurate and incommensurate antiferromagnetic states and could be of importance for other models with imperfect nesting.

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arXiv2013

Metal-insulator transition and phase separation in doped AA-stacked graphene bilayers

We investigate the doping of AA-stacked graphene bilayers. Applying a mean field theory at zero temperature we find that, at half-filling, the bilayer is an antiferromagnetic insulator. Upon doping, the homogeneous phase becomes unstable with respect to phase separation. The separated phases are an undoped antiferromagnetic insulator and a metal with a non-zero concentration of charge carriers. At sufficiently high doping, the insulating areas shrink and disappear, and the system becomes a homogeneous metal. The conductivity changes drastically upon doping, so the bilayer may be used as a switch in electronic devices. The effects of finite temperature are also discussed.

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arXiv2011

Different types of the dimensional crossover in the quasi-one-dimensional spinless fermion systems

It is known that many-body correlations qualitatively modify the properties of a one-dimensional metal. However, for a quasi-one-dimensional metal these correlations are suppressed, at least partially. We study conditions under which the one-dimensional effects significantly influence the dimensional crossover of a quasi-one-dimensional metal. It is proved (i) that even a system with very high anisotropy of the single-particle hopping might behave on both sides of the crossover as an ordinary weakly non-ideal Fermi gas. Further, (ii) to demonstrate well-developed signatures of one-dimensional correlations the system must have extremely (exponentially) high anisotropy. Between cases (i) and (ii) an intermediate regime lies: (iii) the one-dimensional phenomena affect the two-particle susceptibilities, but do not reveal themselves in single-particle quantities. Unlike the normal state properties, (iv) the ordering transition is always very sensitive to the anisotropy: the mean field theory quickly becomes invalid as the anisotropy increases. An expression for the transition temperature is derived. The attributes (i-iv) are used to classify the weakly interacting quasi-one-dimensional fermion systems.

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arXiv2011

Instabilities of the AA-stacked graphene bilayer

Tight-binding calculations predict that the AA-stacked graphene bilayer has one electron and one hole conducting bands, and that the Fermi surfaces of these bands coincide. We demonstrate that as a result of this degeneracy, the bilayer becomes unstable with respect to a set of spontaneous symmetry violations. Which of the symmetries is broken depends on the microscopic details of the system. We find that antiferromagnetism is the more stable order parameter. This order is stabilized by the strong on-site Coulomb repulsion. For an on-site repulsion energy typical for graphene systems, the antiferromagnetic gap can exist up to room temperatures.

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arXiv2011

Phase separation of hydrogen atoms adsorbed on graphene and the smoothness of the graphene-graphane interface

The electronic properties of a graphene sheet with attached hydrogen atoms is studied using a modified Falicov-Kimball model on the honeycomb lattice. It is shown that in the ground state this system separates into two phases: fully hydrogenated graphene (graphane) and hydrogen-free graphene. The graphene-graphane boundary acquires a positive interface tension. Therefore, the graphene-graphane interface becomes a straight line, slightly rippled by thermal fluctuations. A smooth interface may be useful for the fabrication of mesoscopic graphene-based devices.

cond-mat.mes-hall↗

arXiv2011

Majorana fermions in pinned vortices

Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $Δ$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal fluctuations, as long as the temperature remains substantially lower than the critical superconducting temperature. Experimentally, the Majorana state may be detected by measuring the tunneling differential conductance at the center of the Abrikosov vortex. In such an experiment, the Majorana state manifests itself as a zero-bias anomaly separated by a gap, of the order of $Δ$, from the contributions of the nontopological excitations.

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arXiv2011

Electronic properties of mesoscopic graphene structures: charge confinement and control of spin and charge transport

This brief review discusses electronic properties of mesoscopic graphene-based structures. These allow controlling the confinement and transport of charge and spin; thus, they are of interest not only for fundamental research, but also for applications. The graphene-related topics covered here are: edges, nanoribbons, quantum dots, $pn$-junctions, $pnp$-structures, and quantum barriers and waveguides. This review is partly intended as a short introduction to graphene mesoscopics.

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arXiv2011

Evaluation of the two-particle propagator for Hubbard model with the help of Hubbard-I approximation

The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for Hubbard model on two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada [J. Phys. Soc. Jpn. {\bf 76}, 113708 (2007)] in the limit of strong electron-electron interaction. The Hubbard-I predictions are in a good qualitative agreement with the Monte Carlo results. In particular, $d$-wave correlations decay as $c r^{-3}$ ("free electron" behaviour), if separation $r$ exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates coefficient $c$ by a factor of about three. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of $r$.

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arXiv2009

Exact wave functions for an electron on a graphene triangular quantum dot

We generalize the known solution of the Schrödinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the eigenenergies are determined analytically. As an application, we calculate the corrections to the quantum dot's energy levels due to distortions of the carbon-carbon bonds at the edges of the quantum dot.

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