Abstract: We propose an effective potential for an excess electron near the helium liquid-vapor interface that takes into account the diffuseness of the liquid-vapor interface and the classical image potential. The splitting of the first two excited states of the excess electron bound to the helium liquid-vapor interface as a function of an external constant electric field applied perpendicular to the interface is in excellent agreement with recent experiments. The effect of a parallel magnetic field on the energy levels are calculated. Single-electron tunneling of the electron out of its surface state is studied as a function of the electric field applied to the system. We found that the tunneling time has a linear dependence on the electric field.

Abstract: At the interface of electrostatic potential kink profiles, one-dimensional chiral states are found in bilayer graphene (BLG). Such structures can be created by applying an asymmetric potential to the upper and the lower layers of BLG. We found the following: (i) due to the strong confinement by the single kink profile, the unidirectional states are only weakly affected by a magnetic field; (ii) increasing the smoothness of the kink potential results in additional bound states, which are topologically different from those chiral states; and (iii) in the presence of a kink-antikink potential, the overlap between the oppositely moving chiral states results in the appearance of crossing and anticrossing points in the energy spectrum. This leads to the opening of tunable minigaps in the spectrum of the unidirectional topological states.

Abstract: An analytical approach, using the Dirac-Weyl equation, is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. Results are obtained for the infinite-massand zigzag boundary conditions. We found that the energy spectrum of a dot with the zigzag boundary condition exhibits a zero-energy band regardless of the value of the magnetic field, while for the infinite-mass boundary condition, the zero-energy states appear only for high magnetic fields. The analytical results are compared to those obtained from the tight-binding model: (i) we show the validity range of the continuum model and (ii) we find that the continuum model with the infinite-mass boundary condition describes rather well its tight-binding analog, which can be partially attributed to the blurring of the mixed edges by the staggered potential.

Abstract: We present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types in the presence of a perpendicular magnetic field. Results are obtained within the tight-binding (TB) and Dirac models and we discuss which features of the former can be recovered by using the approximations imposed by the latter. Energy levels of graphene quantum rings obtained by diagonalizing the TB Hamiltonian are demonstrated to be strongly dependent on the rings geometry and the microscopical structure of the edges. This makes it difficult to recover those spectra by the existing theories that are based on the continuum (Dirac) model. Nevertheless, our results show that both approaches (i.e., TB and Dirac model) may provide similar results, but only for very specific combinations of ring geometry and edge types. The results obtained by a simplified model describing an infinitely thin circular Dirac ring show good agreement with those obtained for hexagonal and rhombus armchair graphene rings within the TB model. Moreover, we show that the energy levels of a circular quantum ring with an infinite mass boundary condition obtained within the Dirac model agree with those for a ring defined by a ring-shaped staggered potential obtained within the TB model.

Abstract: Within a minimal model, we present analytical expressions for the eigenstates and eigenvalues of carriers confined in quantum rings in monolayer and bilayer graphene. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e., by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearance of Aharonov-Bohm oscillations and of a nonzero gap in the spectrum. Our minimal model gives insight on the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings.

Abstract: The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagatingwave functions describing Schrodinger particles, namely, charge carriers in semiconductor nanostructures within the effective mass approximation, in the presence of Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We also demonstrate that simple modifications to the expanded technique allow us to calculate the time evolution of wave packets describing Dirac particles, which are relevant for the study of transport properties in graphene.

Abstract: Propagation of an electron wave packet through a quantum point contact (QPC) defined by electrostatic gates in bilayer graphene is investigated. The gates provide a bias between the layers, in order to produce an energy gap. If the gates on both sides of the contact produce the same bias, steps in the electron transmission probability are observed, as in the usual QPC. However, if the bias is inverted on one of the sides of the QPC, only electrons belonging to one of the Dirac valleys are allowed to pass, which provides a very efficient valley filtering.

Abstract: The time evolution of a wave packet in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudomagnetic field, on the wave-packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K' Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.

Abstract: We consider a classical system of two-dimensional (2D) charged particles, interacting through a repulsive Yukawa potential exp(-r/λ)/r, and confined in a parabolic channel that limits the motion of the particles in the y direction. Along the x direction, the particles are subject to a periodic potential. The ground-state configurations and the normal-mode spectra of the system are obtained as a function of the periodicity and strength of the periodic potential (V0) and density. An interesting set of tunable ground-state configurations are found, with first- or second-order structural transitions between them. A configuration with particles aligned, perpendicular to the x direction, in each minimum of the periodic potential is obtained for V0 larger than some critical value that has a power-law dependence on the density. The phonon spectrum of different configurations was also calculated. A localization of the modes into a small frequency interval is observed for sufficiently large strength of the periodic potential, and a tunable gap in the phonon spectrum is found as a function of V0.

Abstract: We investigate the effect of opening and closing pathways on the dynamics of electron wave packets in semiconductor quantum rings with different geometries. Our analysis is based on the time evolution of an electron wave packet, within the effective-mass approximation. We demonstrate that opening an extra channel in the quantum ring does not necessarily improve the electron transmission and, depending on the extra channel width, may even reduce it, either due to enhancement of quantum scattering or due to interference. In the latter case, transmission reduction can be controlled through the Aharonov-Bohm phase of the wave function, via an applied magnetic field. It is also shown that, closing one of the channels of the quantum ring, system improves the transmission probability under specific conditions, an effect which is a quantum analog of the Braess paradox.

Abstract: The time evolution of a low-energy two-dimensional Gaussian wave packet in ABC-stacked n-layer graphene (ABC-NLG) is investigated. Expectation values of the position (x, y) of center-of-mass and the total probability densities of the wave packet are calculated analytically using the Green's function method. These results are confirmed using an alternative numerical method based on the split-operator technique within the Dirac approach for ABC-NLG, which additionally allows to include external fields and potentials. The main features of the zitterbewegung (trembling motion) of wave packets in graphene are demonstrated and are found to depend not only on the wave packet width and initial pseudospin polarization, but also on the number of layers. Moreover, the analytical and numerical methods proposed here allow to investigate wave packet dynamics in graphene systems with an arbitrary number of layers and arbitrary potential landscapes.

Abstract: Recent experimental measurements of light absorption in few-layer black phosphorus (BP) revealed a series of high and sharp peaks, interspersed by pairs of lower and broader features. Here, we propose a theoretical model for these excitonic states in few-layer BP within a continuum approach for the in-plane degrees of freedom and a tight-binding approximation that accounts for interlayer couplings. This yields excitonic transitions between different combinations of the subbands created by the coupled BP layers, which leads to a series of high and low oscillator strength excitonic states, consistent with the experimentally observed bright and dark exciton peaks, respectively. The main characteristics of such subband exciton states, as well as the possibility to control their energies and oscillator strengths via applied electric and magnetic fields, are discussed, towards a full understanding of the excitonic spectrum of few-layer BP and its tunability.

Abstract: The interaction of monolayer graphene with specific substrates may break its sublattice symmetry and results in unidirectional chiral states with opposite group velocities in the different Dirac cones (Zarenia et al 2012 Phys. Rev. B 86 085451). Taking advantage of this feature, we propose a valley filter based on a transversal mass kink for low energy electrons in graphene, which is obtained by assuming a defect region in the substrate that provides a change in the sign of the substrate-induced mass and thus creates a non-biased channel, perpendicular to the kink, for electron motion. By solving the time-dependent Schrodinger equation for the tight-binding Hamiltonian, we investigate the time evolution of a Gaussian wave packet propagating through such a system and obtain the transport properties of this graphene-based substrate-induced quantum point contact. Our results demonstrate that efficient valley filtering can be obtained, provided: (i) the electron energy is sufficiently low, i.e. with electrons belonging mostly to the lowest sub-band of the channel, and (ii) the channel length (width) is sufficiently long (narrow). Moreover, even though the transmission probabilities for each valley are significantly affected by impurities and defects in the channel region, the valley polarization in this system is shown to be robust against their presence.