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The distinctive features of the electronic structure of vortex states in superconducting graphene are studied within the Bogolubov-de Gennes theory applied to excitations near the Dirac point. We suggest a scenario describing the subgap spectrum transformation which occurs with a change in the doping level. For an arbitrary vorticity and doping level we investigate the problem of existence of zero energy modes. The crossover to a Caroli -de Gennes -Matricon type of spectrum is studied. 74.78.Na,74.25.Jb Recent exciting developments in transport experiments on graphene [1] have stimulated theoretical studies of possible superconductivity phenomena in this material [2,3,4,5]. A number of unusual features of superconducting state have been predicted, which are closely related to the Dirac-like spectrum of normal state excitations. In particular, the unconventional normal electron dispersion has been shown to result in a nontrivial modification of Andreev reflection [6] and Andreev bound states in Josephson junctions [7]. In this Letter we consider another generic problem illustrating the new physics of Andreev scattering processes in graphene, namely, the electronic spectrum in the core of a vortex that can presumably appear in the superconducting graphene in presence of magnetic field. The electronic vortex structure for Dirac fermions has been previously studied in particle physics for a situation equivalent to the zero doping limit in graphene, when the Dirac point lies exactly at the Fermi level. A number of important results have been obtained, namely, the exact solutions for the zero energy modes [8,9] and the subgap spectrum for some model gap profiles within the vortex core [10]. The problem of zero energy modes has been further addressed in [11,12] for vortices in various condensate phases described by the Dirac theory on a honeycomb lattice. Our goal is to develop a theoretical description of the electronic structure of multiply quantized vortices beyond the zero doping limit and study the transformation of the spectrum under the shift µ of the Fermi level from the Dirac point.The energy spectrum is determined by the vortex winding number (vorticity) n and labeled by the angular momentum ν which is a conserved quantity for an axisymmetric vortex. For zero doping the sub-gap spectrum consists of n zero energy states [8,9]. The states with higher energies lie close to the gap edge ±|∆ 0 |. In the present Letter we demonstrate that, with an increase in doping level µ, the distance between the energy levels decreases, so that more and more states fill the subgap region. The set of low-energy levels gradually transforms into a set of n "spectrum branches" E (i) (ν) where i = 1, . . . , n. If ν is considered as a continuous param-eter, these n energy branches cross the Fermi level [13] as functions of ν. The detailed behavior of the energy spectrum as a function of µ crucially depends on the parity of the winding number. For odd n there exists one branch which intersects zero energy at ν = 0. Its crossing poi...

Theory of electronic transport; scattering mechanisms PACS 73.23.-b -Electronic transport in mesoscopic systems PACS 73.63.-b -Electronic transport in nanoscale materials and structures PACS 74.50.+r -Tunneling phenomena; point contacts, weak links, Josephson effectsAbstract. -The conductance in two-dimensional (2D) normal-superconducting (NS) systems is analyzed in the limit of strong magnetic fields when the transport is mediated by the electronhole states bound to the sample edges and NS interface, i.e., in the Integer Quantum Hall Effect regime. The Andreev-type process of the conversion of the quasiparticle current into the superflow is shown to be strongly affected by the mixing of the edge states localized at the NS and insulating boundaries. The magnetoconductance in 2D NS structures is calculated for both quadratic and Dirac-like normal state spectra. Assuming a random scattering of the edge modes we analyze both the average value and fluctuations of conductance for an arbitrary number of conducting channels.

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one-dimensional Andreev states in a quantum box and (ii) a single vortex in a mesoscopic cylinder.

The magnetocaloric effect in ferromagnet/paramagnet multilayer structures is studied in the framework of the Landau phenomenological theory of phase transitions. The performed estimations demonstrate the possibil ity of achieving record cooling efficiency with such structures.