Abstract: Using an exact-diagonalization approach we show that one- and two-electron InAs quantum dots exhibit an avoided crossing in the energy spectra that is induced by the spin-orbit coupling in the presence of an in-plane external magnetic field. The width of the avoided crossings depends strongly on the orientation of the magnetic field, which reveals the intrinsic anisotropy of the spin-orbit-coupling interactions. We find that for specific orientations of the magnetic field avoided crossings vanish. A value of this orientation can be used to extract the ratio of the strength of Rashba and Dresselhaus interactions. The spin-orbit anisotropy effects for various geometries and orientations of the confinement potential are discussed. Our analysis explains the physics behind the recent measurements performed on a gated self-assembled quantum dot [ S. Takahashi et al. Phys. Rev. Lett. 104 246801 (2010)].

Abstract: We evaluate the transmission and conductance through magnetic barrier structures in bilayer graphene. In particular we consider a magnetic step, single and double barriers, -function barriers, as well as barrier structures that have average magnetic field equal to zero. The transmission depends strongly on the direction of the incident electron or hole wavevector and gives the possibility to construct a direction-dependent wavevector filter. The results contrast sharply with previous results on single-layer graphene. In general, the angular range of perfect transmission becomes drastically wider and the gaps narrower. This perfect transmission range decreases with the number of barriers, the barrier width, and the magnetic field. Depending on the structure, a variety of transmission resonances occur that are reflected in the conductance through the structure.

Abstract: Chiral fermions are responsible for low-temperature properties of vortices in fermionic condensates, both superconducting (charged) and superfluid (neutral). One of the most striking consequences of this fact is that the core of a single-quantum vortex collapses at low temperatures, T -> 0 (i.e., the Kramer-Pesch effect for superconductors), due to the presence of chiral quasiparticles in the vortex-core region. We show that the situation changes drastically for fermionic condensates confined in quasi-one-dimensional and quasi-two-dimensional geometries. Here quantum confinement breaks the chirality of in-core fermions. As a result, instead of the ultimate shrinking, the core of a single-quantum vortex extends at low temperatures, and the condensate profile surprisingly mimics the multiquantum vortex behavior. Our findings are relevant for nanoscale superconductors, such as recent metallic nanoislands on silicon, and also for ultracold superfluid Fermi gases in cigar-shaped and pancake-shaped atomic traps.

Abstract: Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant-multivortex combinations, and states comprising giant antivortices, were found as ground states and their stability was found to be very sensitive on the value of k(F)xi(0), the size of the sample W, and the magnetic flux Phi. By increasing the temperature and/or enlarging the size of the sample, quantum confinement is suppressed and the conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL) theory are recovered. However, contrary to the GL results we found that the states containing symmetry-induced vortex-antivortex pairs are stable over the whole temperature range. It turns out that the inhomogeneous order parameter induced by quantum confinement favors vortex-antivortex molecules, as well as giant vortices with a rich structure in the vortex core-unattainable in the GL domain.

Abstract: We apply density-functional theory to study the adsorption of water clusters on the surface of a graphene sheet and find i) graphene is highly hydrophobic and ii) adsorbed water has very little effect on the electronic structure of graphene. A single water cluster on graphene has a very small average dipole moment which is in contrast with an ice layer that exhibits a strong dipole moment.

Abstract: The time evolution of a wave packet injected into a semiconductor quantum ring is investigated in order to obtain the transmission and reflection probabilities. Within the effective-mass approximation, the time-dependent Schrödinger equation is solved for a system with nonzero width of the ring and leads and finite potential-barrier heights, where we include smooth lead-ring connections. In the absence of a magnetic field, an analysis of the projection of the wave function over the different subband states shows that when the injected wave packet is within a single subband, the junction can scatter this wave packet into different subbands but remarkably at the second junction the wave packet is scattered back into the subband state of the incoming wave packet. If a magnetic field is applied perpendicularly to the ring plane, transmission and reflection probabilities exhibit Aharonov-Bohm (AB) oscillations and the outgoing electrons may end up in different subband states from those of the incoming electrons. Localized impurities, placed in the ring arms, influence the AB oscillation period and amplitude. For a single impurity or potential barrier of sufficiently strong strength, the period of the AB oscillations is halved while for two impurities localized in diametrically opposite points of the ring, the original AB period is recovered. A theoretical investigation of the confined states and time evolution of wave packets in T wires is also made, where a comparison between this system and the lead-ring junction is drawn.