A. V. Rozhkov

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.

Electronic properties of graphene-based bilayer systems

This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental research in bilayer graphene.

Instabilities of the AA-stacked graphene bilayer.

Tight-binding calculations predict that the AA-stacked bilayer graphene has one electron and one hole conducting band, 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. For strong on-site Coulomb interaction we find that antiferromagnetism is the most stable order parameter. For an on-site repulsion energy typical for graphene systems, the antiferromagnetic gap can exist up to room temperature.

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

Electronic spectrum of twisted bilayer graphene

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Tunneling spectrum of a pinned vortex with a robust Majorana state

, 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

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

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Majorana fermions at the edge of superconducting islands

, from the contributions of the nontopological excitations.

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

A.O. Sboychakov, 2 A.L. Rakhmanov, 2, 3, 4 A.V. Rozhkov, 2, 3 and Franco Nori 5 CEMS, RIKEN, Wako-shi, Saitama, 351-0198, Japan Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412 Moscow, Russia Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141700 Russia All-Russia Research Institute of Automatics, Moscow, 127055 Russia Department of Physics, University of Michigan, Ann Arbor, MI 48109-1040, USA

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

(Received 26 August 2013; revised manuscript received 7 November 2013; published 11 February 2014) 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.