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.

Abstract: We performed a numerical simulation of the dynamics of a Gaussian shaped wavepacket inside a small sized quantum ring, smoothly connected to two leads and exposed to a perturbing potential of a biased atomic force microscope tip. Using the Landauer formalism, we calculated conductance maps of this system in the case of single and two subband transport. We explain the main features in the conductance maps as due to the AFM tip influence on the wavepacket phase and amplitude. In the presence of an external magnetic field, the tip modifies the phi(0) periodic Aharonov-Bohm oscillation pattern into a phi(0)/2 periodic Al'tshuler-Aronov-Spivak oscillation pattern. Our results in the case of multiband transport suggest tip selectivity to higher subbands, making them more observable in the total

Abstract: The effect of trigonal warping on the transmission of electrons tunneling through potential barriers in graphene is investigated. We present calculations of the transmission coefficient for single and double barriers as a function of energy, incidence angle and barrier heights. The results show remarkable valley-dependent directional effects for barriers oriented parallel to the armchair or parallel to the zigzag direction. These results indicate that electrostatic gates can be used as valley filters in graphene-based devices.

Abstract: We investigate the formation of quantum confined structures on the surface of a liquid helium film suspended on a nanostructured substrate. We show theoretically that, by nanostructuring the substrate, it is possible to change the geometry of the liquid helium surface, opening the possibility of designing and controlling the formation of valleys with different shapes. By applying an external electric field perpendicular to the substrate plane, surface electrons can be trapped into these valleys, as in a quantum dot. We investigate how the external parameters, such as the electric field strength and the height of the liquid helium bath, can be tuned to control the energy spectrum of the trapped surface electrons.

Abstract: A pseudomagnetic field kink can be realized along a graphene nanoribbon using strain engineering. Electron transport along this kink is governed by snake states that are characterized by a single propagation direction. Those pseudomagnetic fields point towards opposite directions in the K and K' valleys, leading to valley polarized snake states. In a graphene nanoribbon with armchair edges this effect results in a valley filter that is based only on strain engineering. We discuss how to maximize this valley filtering by adjusting the parameters that define the stress distribution along the graphene ribbon.