Topological Phases for Fermionic Cold Atoms on the Lieb Lattice

We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term - a non-Abelian gauge field - and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.Comment: 12 pages, 9 figure

a review

In this review article we describe spin-dependent transport in materials with spin–orbit interaction of Rashba type. We mainly focus on semiconductor heterostructures, however we consider topological insulators, graphene and hybrid structures involving superconductors as well. We start from the Rashba Hamiltonian in a two dimensional electron gas and then describe transport properties of two- and quasi-one-dimensional systems. The problem of spin current generation and interference effects in mesoscopic devices is described in detail. We address also the role of Rashba interaction on localisation effects in lattices with nontrivial topology, as well as on the Ahronov–Casher effect in ring structures. A brief section, in the end, describes also some related topics including the spin-Hall effect, the transition from weak localisation to weak anti localisation and the physics of Majorana fermions in hybrid heterostructures involving Rashba materials in the presence of superconductivity

Massless Dirac-Weyl Fermions in a T_3 Optical Lattice

We propose an experimental setup for the observation of quasi-relativistic massless Fermions. It is based on a T_3 optical lattice, realized by three pairs of counter-propagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T_3 Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudo-spin S=1. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.Comment: 4 pages, 3 figure

Transport properties of an electron-hole bilayer/superconductor hybrid junction

We investigate the transport properties of a junction consisting of an electron-hole bilayer in contact with normal and superconducting leads. The electron-hole bilayer is considered as a semi-metal with two electronic bands. We assume that in the region between the contacts the system hosts an exciton condensate described by a BCS-like model with a gap $\Gamma$ in the quasiparticle density of states. We first discuss how the subgap electronic transport through the junction is mainly governed by the interplay between two kinds of reflection processes at the interfaces: The standard Andreev reflection at the interface between the superconductor and the exciton condensate, and a coherent crossed reflection at the semi-metal/exciton-condensate interface that converts electrons from one layer into the other. We show that the differential conductance of the junction shows a minimum at voltages of the order of $\Gamma/e$. Such a minimum can be seen as a direct hallmark of the existence of the gapped excitonic state

Spin-orbit interaction and snake states in a graphene p-n junction

We study a model of a p-n junction in single-layer graphene in the presence of a perpendicular magnetic field and spin-orbit interactions. By solving the relevant quantum-mechanical problem for a potential step, we determine the exact spectrum of spin-resolved dispersive Landau levels. Close to zero energy, we find a pair of linearly dispersing zero modes, which possess a wave-vector-dependent spin polarization and can be regarded as quantum analogs of spinful snake states. We show that the Rashba spin-orbit interaction, in particular, produces a wave vector shift between the dispersions of these modes with observable interference effects. These effects can in principle provide a way to detect the presence of Rashba spin-orbit interaction and measure its strength. Our results suggest that a graphene p-n junction in the presence of strong spin-orbit interaction could be used as a building block in a spin field-effect transistor

Spin-resolved scattering through spin-orbit nanostructures in graphene

We address the problem of spin-resolved scattering through spin-orbit nanostructures in graphene, i.e., regions of inhomogeneous spin-orbit coupling on the nanometer scale. We discuss the phenomenon of spin-double refraction and its consequences on the spin polarization. Specifically, we study the transmission properties of a single and a double interface between a normal region and a region with finite spin-orbit coupling, and analyze the polarization properties of these systems. Moreover, for the case of a single interface, we determine the spectrum of edge states localized at the boundary between the two regions and study their properties

Electron Scattering in Intrananotube Quantum Dots

Intratube quantum dots showing particle-in-a-box-like states with level spacings up to 200meV are realized in metallic single-walled carbon nanotubes by means of low dose medium energy Ar irradiation. Fourier transform scanning tunneling spectroscopy compared to results of a Fabry-Perot electron resonator model yields clear signatures for inter- and intra-valley scattering of electrons confined between consecutive irradiation-induced defects (inter-defects distance < 10nm). Effects arising from lifting the degeneracy of the Dirac cones within the first Brillouin zone are also observed

Bloch's theory in periodic structures with Rashba's spin-orbit interaction

We consider a two-dimensional electron gas with Rashba's spin-orbit interaction and two in-plane potentials superimposed along directions perpendicular to each other. The first of these potentials is assumed to be a general periodic potential while the second one is totally arbitrary. A general form for Bloch's amplitude is found and an eigen-value problem for the band structure of the system is derived. We apply the general result to the two particular cases in which either the second potential represents a harmonic in-plane confinement or it is zero. We find that for a harmonic confinement regions of the Brillouin zone with high polarizations are associated with the ones of large group velocity.Comment: 6 pages, 5 figure

Ground state features of the Frohlich model

Following the ideas behind the Feynman approach, a variational wave function is proposed for the Fr\"ohlich model. It is shown that it provides, for any value of the electron-phonon coupling constant, an estimate of the polaron ground state energy better than the Feynman method based on path integrals. The mean number of phonons, the average electronic kinetic and interaction energies, the ground state spectral weight and the electron-lattice correlation function are calculated and successfully compared with the best available results.Comment: 6 figure