Topological insulators are characterized by an insulating bulk with a finite band gap and conducting edge or surface states, where charge carriers are protected against backscattering. These states give rise to the quantum spin Hall effect without an external magnetic field, where electrons with opposite spins have opposite momentum at a given edge. The surface energy spectrum of a threedimensional topological insulator is made up by an odd number of Dirac cones with the spin locked to the momentum. The long-sought yet elusive Majorana fermion is predicted to arise from a combination of a superconductor and a topological insulator. An essential step in the hunt for this emergent particle is the unequivocal observation of supercurrent in a topological phase. Here, we present the first measurement of a Josephson supercurrent through a topological insulator. Direct evidence for Josephson supercurrents in superconductor (Nb) - topological insulator (Bi2Te3) - superconductor e-beam fabricated junctions is provided by the observation of clear Shapiro steps under microwave irradiation, and a Fraunhofer-type dependence of the critical current on magnetic field. The dependence of the critical current on temperature and length shows that the junctions are in the ballistic limit. Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a topologically non-trivial two-dimensional surface state. We argue that the ballistic Josephson current is hosted by this surface state despite the fact that the normal state transport is dominated by diffusive bulk conductivity. The lateral Nb-Bi2Te3-Nb junctions hence provide prospects for the realization of devices supporting Majorana fermions

To guide the search for the Majorana fermion, we theoretically study superconductor/topological/superconductor (S/TI/S) junctions in an experimentally relevant regime. We find that the striking features present in these systems, including the doubled periodicity of the Andreev bound states (ABSs) due to tunneling via Majorana states, can still be present at high electron densities. We show that via the inclusion of magnetic layers, this 4π periodic ABS can still be observed in three-dimensional topological insulators, where finite angle incidence usually results in the opening of a gap at zero energy and hence results in a 2π periodic ABS. Furthermore, we study the Josephson junction characteristics and find that the gap size can be controlled and decreased by tuning the magnetization direction and amplitude. These findings pave the way for designing experiments on S/3DTI/S junctions. 74.78.Fk, 74.45.+c, 03.65.Vf with M the magnetization due to the ferromagnet and m = (m x , m y , m z ) the exchange field. σ i are the Pauli

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-energy mode useful for quantum computation. Our main result is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the tunneling conductance of an s-wave proximised three-dimensional topological insulator. We discuss the necessity to incorporate a ferromagnetic insulator to localise the zero-energy bound state to the interface as a Majorana mode.

In 3D topological insulators achieving a genuine bulk-insulating state is an important research topic. Recently, the material system (Bi,Sb) 2 (Te,Se) 3 (BSTS) has been proposed as a topological insulator with high resistivity and a low carrier concentration (Ren et al 2011 Phys. Rev. B 84 165311). Here we present a study to further refine the bulk-insulating properties of BSTS. We have synthesized BSTS single crystals with compositions around x = 0.5 and y = 1.3. Resistance and Hall effect measurements show high resistivity and record low bulk carrier density for the composition Bi 1.46 Sb 0.54 Te 1.7 Se 1.3 . The analysis of the resistance measured for crystals with different thicknesses within a parallel resistor model shows that the surface contribution to the electrical transport amounts to 97% when the sample thickness is reduced to 1 μm. The magnetoconductance of exfoliated BSTS nanoflakes shows 2D weak antilocalization with α ≃ −1 as expected for transport dominated by topological surface states.

Abstractmagnified imageThe surface of a three‐dimensional (3D) topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to the magnetotransport in Bi‐based 3D topological insulators, as well as the superconducting transport properties of hybrid structures consisting of superconductors and these topological insulators. The helical spin‐momentum coupling of the surface state electrons becomes visible in quantum corrections to the conductivity and magnetoresistance oscil‐lations. An analysis will be provided of the reported magnetoresistance, also in the presence of bulk conductivity shunts. Special attention is given to the large and linear magnetoresistance. Superconductivity can be induced in topological superconductors by means of the proximity effect. The induced supercurrents, Josephson effects and current–phase relations will be reviewed. These materials hold great potential in the field of spintronics and the route towards Majorana devices. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)