In superconductor-topological insulator-superconductor hybrid junctions, the barrier edge states are expected to be protected against backscattering, to generate unconventional proximity effects, and, possibly, to signal the presence of Majorana fermions. The standards of proximity modes for these types of structures have to be settled for a neat identification of possible new entities. Through a systematic and complete set of measurements of the Josephson properties we find evidence of ballistic transport in coplanar Al-Bi2Se3-Al junctions that we attribute to a coherent transport through the topological edge state. The shunting effect of the bulk only influences the normal transport. This behavior, which can be considered to some extent universal, is fairly independent of the specific features of superconducting electrodes. A comparative study of Shubnikov -de Haas oscillations and Scanning Tunneling Spectroscopy gave an experimental signature compatible with a two dimensional electron transport channel with a Dirac dispersion relation. A reduction of the size of the Bi2Se3 flakes to the nanoscale is an unavoidable step to drive Josephson junctions in the proper regime to detect possible distinctive features of Majorana fermions.

A superconductor-semiconducting nanowire-superconductor heterostructure in the presence of spin-orbit coupling and magnetic field can support a supercurrent even in the absence of phase difference between the superconducting electrodes. We investigate this phenomenon—the anomalous Josephson effect—employing a model capable of describing many bands in the normal region. We discuss the geometrical and symmetry conditions required to have a finite anomalous supercurrent, and in particular we show that this phenomenon is enhanced when the Fermi level is located close to a band opening in the normal region.

We consider the Kondo effect in Y-junctions of anisotropic XY models in an applied magnetic field along the critical lines characterized by a gapless excitation spectrum. We find that, while the boundary interaction Hamiltonian describing the junction can be recasted in the form of a four-channel, spin-1/2 antiferromagnetic Kondo Hamiltonian, the number of channels effectively participating in the Kondo effect depends on the chain parameters, as well as on the boundary couplings at the junction. The system evolves from an effective four-channel topological Kondo effect for a junction of XX-chains with symmetric boundary couplings into a two-channel one at a junction of three quantum critical Ising chains. The effective number of Kondo channels depends on the properties of the boundary and of the bulk. The XX-line is a "critical" line, where a fourchannel topological Kondo effect can be recovered by fine-tuning the boundary parameter, while along the line in parameter space connecting the XX-line and the critical Ising point the junction is effectively equivalent to a two-channel topological Kondo Hamiltonian. Using a renormalization group approach, we determine the flow of the boundary couplings, which allows us to define and estimate the critical couplings and Kondo temperatures of the different Kondo (pair) channels. Finally, we study the local transverse magnetization in the center of the Y-junction, eventually arguing that it provides an effective tool to monitor the onset of the two-channel Kondo effect.

We find that Kondo resonant conductance can occur in a quantum dot in the Coulomb blockade regime with an even number of electrons N. The contacts are attached to the dot in a pillar configuration, and a magnetic field B( perpendicular) along the axis is applied. B( perpendicular) lifts the spin degeneracy of the dot energies. Usually, this prevents the system from developing the Kondo effect. Tuning B( perpendicular) to the value B(*) where levels with different total spin cross restores both the degeneracy and the Kondo effect. We analyze a dot charged with N = 2 electrons. Coupling to the contacts is antiferromagnetic due to a spin selection rule and, in the Kondo state, the charge is unchanged while the total spin on the dot is S = 1/2.

We study the surface resistivity of a three-dimensional topological insulator when the boundaries exhibit a non trivial curvature. We obtain an analytical solution for a spherical topological insulator, and we show that a non trivial quantum spin connection emerges from the three dimensional band structure. We analyze the effect of the spin connection on the scattering by a bump on a flat surface. Quantum effects induced by the geometry lead to resonances when the electron wavelength is comparable to the size of the bump.Comment: 11 pages, 4 figures, submitte

We employ a path-integral real-time approach to compute the dc conductance and spin polarization for electrons transported across a ballistic quantum ring with Rashba spin-orbit interaction. We use a piecewise semiclassical approximation for the particle orbital motion and solve the spin dynamics exactly by accounting for both Zeeman coupling and spin-orbit interaction at the same time. Within our approach, we are able to study how the interplay between Berry phase, Aharonov Casher phase, Zeeman interaction, and weak localization corrections influences the quantum interference in the conductance within a wide range of externally applied fields. Our results are helpful in interpreting recent measurements of interferometric rings.

We propose an alternative platform to observe Majorana bound states in solid state systems. High critical temperature cuprate superconductors can induce superconductivity, by proximity effect, in quasi one dimensional nanowires with strong spin orbit coupling. They favor a wider and more robust range of conditions to stabilize Majorana fermions due to the large gap values, and offer novel functionalities in the design of the experiments determined by different dispersion for Andreev bound states as a function of the phase difference.Recently there is an increasing interest in topological quantum computation based on Majorana Bound States (MBS's) [1,2]. Majorana Fermions have been predicted in a wide class of low-dimensional solid state devices. Many of these proposals make use of quasi one dimensional superconductors in contact with topological insulators [3] or quasi one-dimensional materials with strong spin orbit interactions [4][5][6][7]. Also helical magnets [8] and other materials [9][10][11][12][13] are considered. In this paper we propose a quite distinctive heterostructure to observe topologically protected MBS's in a solid state device. Our work rests on the physics of S/R/S hybrid structures in which "R" is a quasi one dimensional semiconductor nanowire (NW) with strong Rashba spin orbit coupling (e.g. InAs or InSb) electrically connected to two conventional low T c superconductor leads ( "S" ) [4,5]. Superconductivity is induced in the spin-orbit coupled semiconductor by proximity effect due to the superconducting electrodes. The coexistence of superconductivity and spin-orbit coupling is a key ingredient for the existence of MBS's at the interfaces between the R region and the superconducting S regions.However, despite the considerable theoretical and experimental [14] efforts, some challenges still remain before a real device allowing isolation and manipulation of MBS's in such geometry can be realized. In particular the difficulties of tuning the chemical potential of the semiconductor region µ, controlling the disorder on the bulk gap as well as optimizing the coupling between the different materials [15][16][17] make the realization of such devices extremely difficult.All schemes proposed up to now to generate MBS's substantially use conventional s-wave superconductors to induce superconductivity and a gap ∆ in the R nanowire [1]. The role of superconducting pairing is to relax number conservation, thus allowing for the mixing of particle and hole degrees of freedom. Zeeman spin splitting is required to halve the number of degrees of freedom at low energies, thus generating the elusive neutral (Majorana) excitation. A simple criterion to induce MBS's at S/R interfaces is given in terms of the applied magnetic field B x oriented along the wire, µ and ∆. The inequality to be satisfied can be stated as:. Low critical magnetic fields (H c ) and low gap values characteristic of conventional low Tc superconductors substantially define the limits of the nominal range of dynamical parameters required to...

Linear conductance across a large quantum dot via a single level epsilon(0) with large hybridization to the contacts is strongly sensitive to quasibound states localized in the dot and weakly coupled to epsilon(0). The conductance oscillates with the gate voltage due to interference of the Fano type. At low temperature and Coulomb blockade, Kondo correlations damp the oscillations on an extended range of gate voltage values, by freezing the occupancy of the epsilon(0) level itself. As a consequence, the antiresonances of Fano origin are washed out. The results are in good correspondence with experimental data for a large quantum dot in the semiopen regime.