Topological superconductivity in lead nanowires

Superconductors with an odd number of bands crossing the Fermi energy have topologically protected Andreev states at interfaces, including Majorana states in one dimensional geometries. Superconductivity, a low number of 1D channels, large spin orbit coupling, and a sizeable Zeeman energy, are present in lead nanowires produced by nanoindentation of a Pb tip on a Pb substrate, in magnetic fields higher than the Pb bulk critical field. A number of such devices have been analyzed. In some of them, the dependence of the critical current on magnetic field, and the Multiple Andreev Reflections observed at finite voltages, are compatible with the existence of topological superconductivity

Orthogonality catastrophe and Kondo effect in graphene

Anderson's orthogonality catastrophe in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed, due to the vanishing density of states at the Dirac point. In the presence of preexisting localized states at the Dirac energy, the orthogonality catastrophe shows similar features to those found in normal metals with a finite density of states at the Fermi level. The implications for the Kondo effect induced by magnetic impurities, and for the Fermi edge singularities in tunneling processes are also discussed.Comment: 7 pages, 7 figure

Many body effects in finite metallic carbon nanotubes

The non homogeneity of the charge distribution in a carbon nanotube leads to the formation of an excitonic resonance, in a similar way to the one observed in X-ray absorption in metals. As a result, a positive anomaly at low bias appears in the tunnelling density of states. This effect depends on the screening of the electron--electron interactions by metallic gates, and it modifies the coupling of the nanotube to normal and superconducting electrodes.Comment: 5 page

Electron-electron interaction and charging effects in graphene quantum dots

We analyze charging effects in graphene quantum dots. Using a simple model, we show that, when the Fermi level is far from the neutrality point, charging effects lead to a shift in the electrostatic potential and the dot shows standard Coulomb blockade features. Near the neutrality point, surface states are partially occupied and the Coulomb interaction leads to a strongly correlated ground state which can be approximated by either a Wigner crystal or a Laughlin like wave function. The existence of strong correlations modify the transport properties which show non equilibrium effects, similar to those predicted for tunneling into other strongly correlated systems.Comment: Extended version accepted for publication at Phys. Rev.

Energy spectrum and Landau levels in bilayer graphene with spin-orbit interaction

We present a theoretical study of the bandstructure and Landau levels in bilayer graphene at low energies in the presence of a transverse magnetic field and Rashba spin-orbit interaction in the regime of negligible trigonal distortion. Within an effective low energy approach (L\"owdin partitioning theory) we derive an effective Hamiltonian for bilayer graphene that incorporates the influence of the Zeeman effect, the Rashba spin-orbit interaction, and inclusively, the role of the intrinsic spin-orbit interaction on the same footing. Particular attention is spent to the energy spectrum and Landau levels. Our modeling unveil the strong influence of the Rashba coupling $\lambda_R$ in the spin-splitting of the electron and hole bands. Graphene bilayers with weak Rashba spin-orbit interaction show a spin-splitting linear in momentum and proportional to $\lambda_R$, but scales inversely proportional to the interlayer hopping energy $\gamma_1$. However, at robust spin-orbit coupling $\lambda_R$ the energy spectrum shows a strong warping behavior near the Dirac points. We find the bias-induced gap in bilayer graphene to be decreasing with increasing Rashba coupling, a behavior resembling a topological insulator transition. We further predict an unexpected assymetric spin-splitting and crossings of the Landau levels due to the interplay between the Rashba interaction and the external bias voltage. Our results are of relevance for interpreting magnetotransport and infrared cyclotron resonance measurements, including also situations of comparatively weak spin-orbit coupling.Comment: 25 pages, 5 figure

Nanosized superconducting constrictions

Nanowires of lead between macroscopic electrodes are produced by means of an STM. Magnetic fields may destroy the superconductivity in the electrodes, while the wire remains in the superconducting state. The properties of the resulting microscopic Josephson junctions are investigated.Comment: 3 pages,3 eps figures include

Theoretical Aspects of the Fractional Quantum Hall Effect in Graphene

We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a high-energy sector, whereas the low-energy excitations only involve the same level, such that the kinetic energy (of the Landau level) is an unimportant constant. Two prominent effects emerge in this limit of strong electronic correlations: generalised quantum Hall ferromagnetic states that profit from the approximate four-fold spin-valley degeneracy of graphene's Landau levels and the fractional quantum Hall effect. Here, we discuss these effects in the framework of an SU(4)-symmetric theory, in comparison with available experimental observations.Comment: 12 pages, 3 figures; review for the proceedings of the Nobel Symposium on Graphene and Quantum Matte

Tailoring the thermal Casimir force with graphene

The Casimir interaction is omnipresent source of forces at small separations between bodies, which is difficult to change by varying external conditions. Here we show that graphene interacting with a metal can have the best known force contrast to the temperature and the Fermi level variations. In the distance range 50–300 nm the force is measurable and can vary a few times for graphene with a bandgap much larger than the temperature. In this distance range the main part of the force is due to the thermal fluctuations. We discuss also graphene on a dielectric membrane as a technologically robust configuration

Low temperature properties of a quantum particle coupled to dissipative environments

We study the dynamics of a quantum particle coupled to dissipative (ohmic) environments, such as an electron liquid. For some choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first order transition, between strongly and weakly localized regimes.Comment: 10 page