Superconductivity involving topological Dirac electrons has recently been proposed as a platform between concepts in high-energy and condensed-matter physics. It has been predicted that supersymmetry and Majorana fermions, both of which remain elusive in particle physics, may be realized through emergent particles in these particular superconducting systems. Using artificially fabricated topological-insulator-superconductor heterostructures, we present direct spectroscopic evidence for the existence of Cooper pairing in a weakly interacting half Dirac gas. Our studies reveal that two dimensional topological superconductivity in a helical Dirac gas is distinctly di erent from that in an ordinary two-dimensional superconductor in terms of the spin degrees of freedom of electrons. We further show that the pairing of Dirac electrons can be suppressed by timereversal symmetry-breaking impurities, thereby removing the distinction. Our demonstration and momentum-space imaging of Cooper pairing in a half-Dirac-gas two-dimensional topological superconductor serve as a critically important platform for future testing of fundamental physics predictions such as emergent supersymmetry and topological quantum criticality. R ealization of novel superconductivity is one of the central themes in condensed matter physics in general 1-24 . Superconductivity is a collective phenomenon, where electrons moving to the opposite directions (±k) form dynamically bound pairs, resulting in a Cooper pair gas. In an ordinary superconductor, the conduction electrons that move along a certain direction have both spin-up and spin-down electrons available for the Cooper pairing. The superconductivity observed so far, including in the conventional s-wave BCS superconductors as well as the cuprate or heavy fermion d-wave superconductors, all share this property. Recently, the discovery of 3D topological insulators (TIs) in bismuth-based semiconducting compounds has attracted much interest in condensed matter physics. In these TI materials, the bulk has a full energy gap whereas the surface exhibits an odd number of Dirac-cone electronic states, where the spin of the surface electrons is uniquely locked to their momentum 1,2 . Therefore, at any given surface of a TI, the surface electrons moving in one direction (for example, +k) will have only spin-up electrons available whereas those of moving to −k have only spin-down electrons available. This is in contrast to the Fermi level electronic states in an ordinary superconductor. This distinction can give rise to a wide range of exotic physics. Recently, a number of theories have highlighted these possibilities from both the fundamental physics and applications point of view 4-10 . For example, both supersymmetry and Majorana fermions are interesting physics phenomena predicted in high-energy theories that remain unobserved in particle physics experiments. And it has been theoretically predicted, very recently, that such new physics can be realized in a condensed matter setting 4,6 , if superconductiv...

Coupling the surface state of a topological insulator to an s-wave superconductor is predicted to produce the long-sought Majorana quasiparticle excitations. However, superconductivity has not been measured in surface states when the bulk charge carriers are fully depleted, that is, in the true topological regime relevant for investigating Majorana modes. Here we report measurements of d.c. Josephson effects in topological insulator-superconductor junctions as the chemical potential is moved through the true topological regime characterized by the presence of only surface currents. We compare our results with three-dimensional quantum transport simulations, and determine the effects of bulk/surface mixing, disorder and magnetic field; in particular, we show that the supercurrent is largely carried by surface states, due to the inherent topology of the bands, and that it is robust against disorder. Our results thus clarify key open issues regarding the nature of supercurrents in topological insulators.

Aharonov-Bohm oscillations effectively demonstrate coherent, ballistic transport in mesoscopic rings and tubes. In three-dimensional topological insulator nanowires, they can be used to not only characterize surface states but also to test predictions of unique topological behaviour. Here we report measurements of Aharonov-Bohm oscillations in (Bi 1.33 Sb 0.67 )Se 3 that demonstrate salient features of topological nanowires. By fabricating quasi-ballistic three-dimensional topological insulator nanowire devices that are gate-tunable through the Dirac point, we are able to observe alternations of conductance maxima and minima with gate voltage. Near the Dirac point, we observe conductance minima for zero magnetic flux through the nanowire and corresponding maxima (having magnitudes of almost a conductance quantum) at magnetic flux equal to half a flux quantum; this is consistent with the presence of a low-energy topological mode. The observation of this mode is a necessary step towards utilizing topological properties at the nanoscale in post-CMOS applications.

Ultracold and quantum degenerate gases held near conductive surfaces can serve as sensitive, high resolution, and wide-area probes of electronic current flow. Previous work has imaged transport around grain boundaries in a gold wire by using ultracold and Bose-Einstein condensed atoms held microns from the surface with an atom chip trap. We show that atom chip microscopy may be applied to useful purpose in the context of materials exhibiting topologically protected surface transport. Current flow through lithographically tailored surface defects in topological insulators (TI)---both idealized and with the band-structure and conductivity typical of Bi$_{2}$Se$_{3}$---is numerically calculated. We propose that imaging current flow patterns enables the differentiation of an ideal TI from one with a finite bulk--to--surface conductivity ratio, and specifically, that the determination of this ratio may be possible by imaging transport around trenches etched into the TI's surface.Comment: Extensively rewritten, better introduction. 12 pages, 10 figure

We investigate the superfluid properties of disordered double layer graphene systems using the non-equilibrium Green's function formalism. The complexity of such a structure makes it imperative to study the effects of lattice vacancies which will inevitably arise during fabrication. We present and compare room temperature performance characteristics for both ideal and disordered double layer graphene systems in an effort to illustrate the behavior of a Bose-Einstein condensate in the presence of lattice defects under non-equilibrium conditions. We find that lattice vacancies spread throughout the top layer past the coherence length have a reduced effect compared to the ideal case. However, vacancies concentrated near the metal contacts within the coherence length significantly alter the interlayer superfluid transport properties.