Crossed Andreev reflection in a graphene bipolar transistor

We investigate the crossed Andreev reflections between two graphene leads connected by a narrow superconductor. When the leads are respectively of the n-and p- type, we find that electron elastic cotunneling and local Andreev reflection are both eliminated even in the absence of any valley-isospin or spin polarizations. We further predict oscillations of both diagonal and cross conductances as a function of the distance between the graphene-superconductor interfaces.Comment: 4 pages, 4 figures. Accepted in Physical Review Letter

Introduction to Dirac materials and topological insulators

We present a short pedagogical introduction to the physics of Dirac materials, restricted to graphene and two- dimensional topological insulators. We start with a brief reminder of the Dirac and Weyl equations in the particle physics context. Turning to condensed matter systems, semimetallic graphene and various Dirac insulators are introduced, including the Haldane and the Kane-Mele topological insulators. We also discuss briefly experimental realizations in materials with strong spin-orbit coupling.Comment: 24 pages, 8 figures; review submitted to topical issue of "Comptes Rendus de l'Acad\'emie des Sciences (Physique)" devoted to topological insulators and Dirac matter. Pre-publication version; comments are invite

Andreev spectroscopy of doped HgTe quantum wells

We investigate the Andreev reflection process in high-mobility HgTe/CdTe quantum wells. We find that Andreev conductance probes the dynamics of massive 2+1 Dirac fermions, and that both specular Andreev reflection and retroreflection can be realized even in presence of a large mismatch between the Fermi wavelengths at the two sides of the normal/superconducting junction.Comment: 7 pages, 6 figure

Spin Hall effect at interfaces between HgTe/CdTe quantum wells and metals

We study the spin-dependent transmission through interfaces between a HgTe/CdTe quantum well (QW) and a metal - both for the normal metal and the superconducting case. Interestingly, we discover a new type of spin Hall effect at these interfaces that happens to exist even in the absence of structure and bulk inversion asymmetry within each subsystem (i.e. the QW and the metal). Thus, this is a pure boundary spin Hall effect which can be directly related to the existence of exponentially localized edge states at the interface. We demonstrate how this effect can be measured and functionalized for an all-electric spin injection into normal metal leads.Comment: 7 pages, 6 figure

Josephson coupling through ferromagnetic heterojunctions with noncollinear magnetizations

We study the Josephson effect in clean heterojunctions that consist of superconductors connected through two metallic ferromagnets with insulating interfaces. We solve the scattering problem based on the Bogoliubov--de Gennes equation for any relative orientation of in-plane magnetizations, arbitrary transparency of interfaces, and mismatch of Fermi wave vectors. Both spin singlet and triplet superconducting correlations are taken into account, and the Josephson current is calculated as a function of the ferromagnetic layers thicknesses and of the angle $\alpha$ between their magnetizations. We find that the critical Josephson current $I_c$ is a monotonic function of $\alpha$ when the junction is far enough from $0-\pi$ transitions. This holds when ferromagnets are relatively weak. For stronger ferromagnets, variation of $\alpha$ induces switching between 0 and $\pi$ states and $I_c(\alpha)$ is non-monotonic function, displaying characteristic dips at the transitions. However, the non-monotonicity is the effect of a weaker influence of the exchange potential in the case of non-parallel magnetizations. No substantial impact of spin-triplet superconducting correlations on the Josephson current has been found in the clean limit. Experimental control of the critical current and $0-\pi$ transitions by varying the angle between magnetizations is suggested.Comment: 7 pages, 8 figure

Long ranged singlet proximity effect in ferromagnetic nanowires

Recently a long ranged superconductor/ferromagnet (S/F) proximity effect has been reported in Co crystalline nanowires [1, Nature, 6 389 (2010)]. Since the authors of [1] take care to avoid the existence of magnetic domains, the triplet character of the long ranged proximity effect is improbable. Here we demonstrate that in the one-dimensional ballistic regime the standard singlet S/F proximity effect becomes long ranged. We provide an exact solution for the decay of the superconducting correlations near critical temperature ($T_{c}$) and for arbitrary impurities concentration. In particular we find a specific regime, between the diffusive and ballistic ones, where the decay length is simply the electronic mean-free path. Finally possible experiments which could permit to elucidate the nature of the observed long ranged proximity effect in Co nanowires are discussed.Comment: 4 page

Non uniform superconductivity in wires with strong spin-orbit coupling

We study theoretically the onset of nonuniform superconductivity in a one-dimensional single wire in presence of Zeeman (or exchange field) and spin-orbit coupling. Using the Green's function formalism, we show that the spin-orbit coupling stabilizes modulated superconductivity in a broad range of temperatures and Zeeman fields. We investigate the anisotropy of the temperature-Zeeman field phase diagram, which is related to the orientation of the Zeeman field. In particular, the inhomogeneous superconducting state disappears if this latter field is aligned or perpendicular to the wire direction. We identify two regimes corresponding to weak and strong spin-orbit coupling respectively. The wave-vector of the modulated phase is evaluated in both regimes. The results also pertain for quasi-1D superconductors made of weakly coupled 1D chains.Comment: 10 pages, 3 figure

Electronic Raman scattering on under-doped Hg-1223 high-Tc superconductors:investigations on the symmetry of the order parameter

In order to obtain high quality, reliable electronic Raman spectra of a high-Tc superconductor compound, we have studied strongly under-doped HgBa2Ca2Cu3O8+d. This choice was made such as to i)minimize oxygen disorder in the Hg-plane generated by oxygen doping ii) avoid the need of phonon background subtraction from the raw data iii)eliminate traces of parasitic phases identified and monitored on the crystal surface. Under these experimental conditions we are able to present the pure electronic Raman response function in the B2g, B1g, A1g+B2g and A1g+B1g channels. The B2g spectrum exhibits a linear frequency dependence at low energy whereas the B1g one shows a cubic-like dependence. The B2g and B1g spectra display two well defined maxima at 5.6kBTc and 9kBTc respectively. In mixed A1g channels an intense electronic peak centered around 6.4 kBTc is observed. The low energy parts of the spectra correspond to the electronic response expected for a pure dx2-y2 gap symmetry and can be fitted up to the gap energy for the B1g channel. However, in the upper parts, the relative position of the B1g and B2g peaks needs expanding the B2g Raman vertex to second order Fermi surface harmonics to fit the data with the dx2-y2 model. The sharper and more intense A1g peak appears to challenge the Coulomb screening efficiency present for this channel. As compared to previous data on more optimally doped, less stoichiometric Hg-1223 compounds, this work reconciles the electronic Raman spectra of under- doped Hg-1223 crystals with the dx2-y2 model, provided that the oxygen doping is not too strong. This apparent extreme sensitivity of the electronic Raman spectra to the low lying excitations induced by oxygen doping in the superconducting state is emphasized here and remains an open question.Comment: 12 pages, 5 figure

Contact resistance and shot noise in graphene transistors

Potential steps naturally develop in graphene near metallic contacts. We investigate the influence of these steps on the transport in graphene Field Effect Transistors. We give simple expressions to estimate the voltage-dependent contribution of the contacts to the total resistance and noise in the diffusive and ballistic regimes.Comment: 6 pages, 4 figures; Figs 3 and 4 completed and appendix adde