A quantitative analysis of a recent model of high-temperature superconductors based on an interlayer tunneling mechanism is presented. This model can account well for the observed magnitudes of the high transition temperatures in these materials and implies a gap that does not change sign, can be substantially anisotropic, and has the same symmetry as the crystal. The experimental consequences explored so far are consistent with the observations.

We investigate the conductance spectra of a normal/superconductor graphene junction using the extended Blonder-Tinkham-Klapwijk formalism, considering pairing potentials that are both conventional (isotropic swave) and unconventional (anisotropic d-wave). In particular, we study the full crossover from normal to specular Andreev reflection without restricting ourselves to special limits and approximations, thus expanding results obtained in previous work. In addition, we investigate in detail how the conductance spectra are affected if it is possible to induce an unconventional pairing symmetry in graphene, for instance a d-wave order parameter. We also discuss the recently reported conductance-oscillations that take place in normal/superconductor graphene junctions, providing both analytical and numerical results.

We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zeroenergy surface state in the d xy -wave case becomes a Majorana fermion, in contrast to the situation realized in the topologically trivial high-T c cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of this field is shown to strongly influence the transport properties, in contrast to the case without TI. We predict an experimental signature of the Majorana states via conductance spectroscopy. PACS numbers:Topological insulators represent a new state of matter which presently is generating much interest [1][2][3][4]. While being insulating in the bulk due to a charge excitation gap, spindependent conducting channels are formed at the edges or surfaces of such materials. These states form as Kramer pairs which are topologically protected, persisting in the presence of disorder as long as time-reversal symmetry is preserved. The allure of topological insulators stems not only from their obvious interest from a fundamental physics point of view, but also because they may find use in spintronics [5]. Recent experiments have observed the surface Dirac states characteristic for 3D topological insulators [6].Another motivation for studying topological insulators is that they provide an arena for excitations that satisfy nonAbelian statistics: so-called Majorana fermions [7]. Elementary excitations with non-Abelian statistics form a centerpiece in recent proposals for topological quantum computation [8]. Majorana fermions have been shown to exist as surface states at the junction between a superconductor (S) and ferromagnetic insulator (FI) deposited on a topological insulator due to the proximity effect [9][10][11]. The formation of Majorana states at the interface between a superconductor and a topological insulator [12,13] and at the boundary of superfluid 3 He-B [14] has also been proposed. Very recently, an experimental study reported the observation of doping-induced superconductivity in the topological insulator (TI) Bi 2 Se 3 [15].By depositing superconducting materials with an unconventional pairing symmetry on top of a TI, an exciting prospect of an interplay between the internal phase of the superconducting order parameter ∆ and Majorana states opens up. In this Letter, we investigate how spin-triplet and spinsinglet d-wave pairing interact with the environment of a TI. We find that spin-triplet pairing universally gives rise to gapless excitations and that both bound-states and Andreev reflection are strongly suppressed. For spin-singlet pairing, we find that the zero-energy surface states in the d xy -wave case are now Majorana fermions in contrast to the case of the topologically trivial case of the high-T c cuprates. Several...

We study how the surface states in the strong topological insulator Bi 2 Se 3 are influenced by finite size effects and compare our results with those recently obtained for two-dimensional topological insulator HgTe. We demonstrate two important distinctions: ͑i͒ contrary to HgTe, the surface states in Bi 2 Se 3 display a remarkable robustness towards decreasing the width L down to a few nm thus ensuring that the topological surface states remain intact and ͑ii͒ the gapping due to the hybridization of the surface states features an oscillating exponential decay as a function of L in Bi 2 Se 3 in sharp contrast to HgTe. Our findings suggest that Bi 2 Se 3 is suitable for nanoscale applications in quantum computing or spintronics. Also, we propose a way to experimentally detect both of the predicted effects.

Although hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical properties, including spatial order. To date, the structure of dense hydrogen remains experimentally elusive. Recent studies of the melting curve of hydrogen indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report a topological analysis of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a superconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids.