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

Dynamical response of dissipative helical edge states

Quantum spin Hall insulators are characterized by topologically protected counterpropagating edge states. Here we study the dynamical response of these helical edge states under a time-dependent flux biasing, in the presence of a heat bath. It is shown that the relaxation time of the edge carriers can be determined from a measurement of the dissipative response of topological insulator disks. The effects of various perturbations, including Zeeman coupling and disorder, are also discussed.Comment: 12 page

From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

We consider one-dimensional topological insulators hosting fractionally charged midgap states in the presence and absence of induced superconductivity pairing. Under the protection of a discrete symmetry, relating positive and negative energy states, the solitonic midgap states remain pinned at zero energy when superconducting correlations are induced by proximity effect. When the superconducting pairing dominates the initial insulating gap, Majorana fermion phases develop for a class of insulators. As a concrete example, we study the Creutz model with induced s-wave superconductivity and repulsive Hubbard-type interactions. For a finite wire, without interactions, the solitonic modes originating from the nonsuperconducting model survive at zero energy, revealing a fourfold-degenerate ground state. However, interactions break the aforementioned discrete symmetry and completely remove this degeneracy, thereby producing a unique ground state which ischaracterized by a topological bulk invariant with respect to the product of fermion parity and bond inversion. In contrast, the Majorana edge modes are globally robust to interactions. Moreover, the parameter range for which a topological Majorana phase is stabilized expands when increasing the repulsive Hubbard interaction. The topological phase diagram of the interacting model is obtained using a combination of mean-field theory and density matrix renormalization group techniques.Comment: 20 pages, 20 figure

Anomalous fluctuation regimes at the FFLO transition

Recently some experimental evidences have been obtained in favour of the existence of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state in heavy-fermion superconductor CeCoIn_{5} and organic superconductor -(BETS)_{2}FeCl_{4}. However the unambiguous identification of FFLO state remains very difficult. We present the theoretical studies of the Gaussian fluctuations near the tricritical point (where the FFLO modulation appears) and demonstrate that the behavior of the fluctuational specific heat, paraconductivity and diamagnetism is qualitatively different from the usual superconducting transition. Special values of the critical exponent and the crossovers between different fluctuational regimes may provide a unique test for the FFLO state appearance.Comment: 6 pages, 2 figures. Work supported by ANR Extreme Conditions Correlated Electrons (ANR-06-BLAN-0220

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

Higgs amplitude mode in ballistic superconducting hybrid junctions

In superconductors (SC), the Higgs amplitude mode is a coherent oscillation of the order parameter typically generated by THz laser irradiation. In this paper we propose to probe the Higgs mode using electronic transport in ballistic superconducting hybrid devices. We first confirm the existence of a non-zero amplitude mode in the clean case using the Keldysh-Eilenberger formalism. We then investigate two different geometries, respectively a normal-insulating-superconductor (NIS) tunnel junction and a NSN junction with transparent interfaces, the superconductor being irradiated in both situations. In the NIS case, the Higgs manifests itself in the second-order AC current response which is resonant at the Higgs frequency. In the NSN case, the DC differential conductance allows to probe the gaps generated by the Higgs mode in the Floquet spectrum.Comment: 13 pages, 8 figure