Quantum interference of electrons in a ring: tuning of the geometrical phase

Spin polarized bound states in the continuum in open Aharonov-Bohm rings with the Rashba spin-orbit interaction

We consider the trapping of electrons with a definite spin polarization by bound states in the continuum (BSC) in the open Aharonov-Bohm rings in the presence of the Rashba spin-orbit interaction (RSOI). Neglecting the Zeeman term we show the existence of BSCs in the one-dimensional ring when the eigenstates of the closed ring are doubly degenerate. With account of the Zeeman term BSCs occur only at the points of threefold degeneracy. The BSCs are found in the parametric space of flux and RSOI strength in close pairs with opposite spin polarization. Thereby the spin polarization of electrons transmitted through the ring can be altered by minor variation of magnetic or electric field at the vicinity of these pairs. Numerical simulations of the two-dimensional open ring show similar results for the BSCs. Encircling the BSC points in the parametric space of the flux and the RSOI constant gives rise to a geometric phase.

Quantum transport in Rashba spin-orbit materials: 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.

Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices

The scattering of Dirac electrons by topological defects could be one of the most relevant sources of resistance in graphene and at the boundary surfaces of a three-dimensional topological insulator (3D TI). In the long wavelength, continuous limit of the Dirac equation, the topological defect can be described as a distortion of the metric in curved space, which can be accounted for by a rotation of the Gamma matrices and by a spin connection inherited with the curvature. These features modify the scattering properties of the carriers. We discuss the self-energy of defect formation with this approach and the electron cross-section for intra-valley scattering at an edge dislocation in graphene, including corrections coming from the local stress. The cross-section contribution to the resistivity, ρ, is derived within the Boltzmann theory of transport. On the same lines, we discuss the scattering of a screw dislocation in a two-band 3D TI, like Bi_1-xSb_x, and we present the analytical simplified form of the wavefunction for gapless helical states bound at the defect. When a 3D TI is sandwiched between two even-parity superconductors, Dirac boundary states acquire superconductive correlations by proximity. In the presence of a magnetic vortex piercing the heterostructure, two Majorana states are localized at the two interfaces and bound to the vortex core. They have a half integer total angular momentum each, to match with the unitary orbital angular momentum of the vortex charge.

Coupled quantum dot-ring structures by droplet epitaxy

The fabrication, by pure self-assembly, of GaAs/AlGaAs dot-ring quantum nanostructures is presented. The growth is performed via droplet epitaxy, which allows for the fine control, through As flux and substrate temperature, of the crystallization kinetics of nanometer scale metallic Ga reservoirs deposited on the surface. Such a procedure permits the combination of quantum dots and quantum rings into a single, multi-functional, complex quantum nanostructure.

Spin-polarized transport through an Aharonov-Bohm interferometer embedded with a quantum dot molecule

We propose an Aharonov-Bohm interferometer with a quantum dot molecule embedded in one arm and study the spin-dependent transport due to the interplay of the Fano and Rashba effects. It is found that the Fano resonances of the molecular states exhibit opposite directions of asymmetric tails with one being from peak to dip and the other from dip to peak. The Rashba spin-orbit interaction induces a spin-dependent phase, making the two Fano dips overlap for one spin component of conductance and the two Fano peaks overlap for the other spin component. Both the direction and magnitude of the spin polarization of the conductance are easily controlled and manipulated through the Rashba parameter and interdot coupling strength. In addition, spin accumulations with opposite signs can be generated in the two quantum dots.