We consider the proximity effect between a singlet s-wave superconductor and the edge of a Quantum Spin Hall (QSH) topological insulator. We establish that Andreev reflection at a QSH edge state/superconductor interface is perfect while nonlocal Andreev processes through the superconductor are totally suppressed. We compute the corresponding conductance and noise.The prediction [1] and the observation [2,3] of the Quantum Spin Hall (QSH) state in mercury telluride (HgTe/CdTe) heterostructures have triggered a great deal of excitation in the condensed matter community [4][5][6] since the QSH state realizes a two dimensional (2D) topologically ordered phase in the absence of magnetic field. The QSH state is distinguished from ordinary band insulators by the presence of a one-dimensional metal along its edge [7]. Owing to the dominant role of the spin-orbit interaction, this edge state provides a unique strictly one-dimensional metal where the spin is tied to the direction of motion of the carriers [8]. This so-called helical property and the associated time-reversal symmetry imply the absence of backscattering on non magnetic impurities.So far the existence of the helical liquid has been confirmed by multiterminal transport measurements performed with normal leads [2,3]. Since the QSH state exists under zero magnetic field, in contrast to the integer and fractional quantum Hall states, it can also be probed by the powerful methods of superconducting proximity effect [9]. Along these lines, Andreev spectroscopy has been recently suggested to characterize the quasi-relativistic dynamics of 2D bulk carriers in doped HgTe/CdTe quantum wells [10]. Furthermore helical liquids might also be useful to analyze the entanglement of electrons injected from a singlet s−wave superconductor [11,12].In this Rapid Communication, we theoretically investigate the edge transport of a Quantum Spin Hall insulator in presence of a single superconducting probe. As a result of helicity conservation and absence of backscattering channel, we find that an electron can be either Andreev reflected as a hole, or transmitted as an electron. In a standard metal or in a carbon nanotube, there would be two additional possibilities whereby the electron can be reflected as an electron, or transmitted as a hole [13][14][15][16][17][18][19]. We compute the conductance and the noise associated to this partitioning in two outgoing channels, instead of four channels in standard 1D metals. The related experiments could be implemented readily using a side superconductor contacted to current HgTe/CdTe

International audienceA continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semimetal through a semi-Dirac phase toward a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy

We consider the dc transport properties of topological insulator surface states in the presence of uncorrelated point-like disorder, both in the classical and quantum regimes. The dc conductivity of those two-dimensional surface states depends strongly on the amplitude of the hexagonal warping of their Fermi surface. A perturbative analysis of the warping is shown to fail to describe the transport in Bi 2 Se 3 over a broad range of experimentally available Fermi energies, and in Bi 2 Te 3 for the higher Fermi energies. Hence we develop a fully non-perturbative description of these effects. In particular, we find that the dependence of the warping amplitude on the Fermi energy manifests itself in a strong dependence of the diffusion constant on this Fermi energy, leading to several important experimental consequences. Moreover, the combination of a strong warping with an in-plane Zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped Dirac surface states.