Abstract: The superconducting state. of a thin superconducting disk with a hole is studied within the, nonlinear Ginzburg-Landau theory in which the demagnetization effect is accurately taken into account. We find that the flux through the hole is not quantized, the superconducting state is stabilized with increasing size of the hole for fixed radius of the disk, and a transition to a multivortex state is found if the disk is sufficiently large. Breaking the circular symmetry through a non-central-location of the hole in the disk favors the multivortex state.

Abstract: The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled nonlinear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large intervortex separations that are available in the literature. We propose empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter.

Abstract: Using time-dependent Ginzburg-Landau theory, we study the dynamic properties of a rectangular superconducting loop, which are found to depend on the position of the current leads. For asymmetric positioning of the leads, different kinetic inductance of the two paths for injected electric current leads to different critical conditions in the two branches. System self-regulates by allowing vortex entry, as vortex currents bring equilibration between the two current flows and the conventional resistive state can be realized. We also demonstrate that individual vortex entry in the loop can be detected by measuring the voltage between normal-metal leads, for applied currents comparable in magnitude to the screening currents.

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.

Abstract: We investigate the dynamics of a charged particle moving in a graphene layer and in a two-dimensional electron gas, where it obeys the Dirac and the Schrödinger equations, respectively. The charge carriers are described as Gaussian wavepackets. The dynamics of the wavepackets is studied numerically by solving both quantum-mechanical and relativistic equations of motion. The scattering of such wavepackets by step-like magnetic and potential barriers is analysed for different values of wavepacket energy and width. We find: (1) that the average position of the wavepacket does not coincide with the classical trajectory, and (2) that, for slanted incidence, the path of the centre of mass of the wavepacket does not have to penetrate the barrier during the scattering process. Trembling motion of the charged particle in graphene is observed in the absence of an external magnetic field and can be enhanced by a substrate-induced mass term.

Abstract: We show that the angular range of the transmission through magnetic barrier structures can be efficiently controlled in single-layer and bilayer graphenes and this renders the structures efficient wavevector filters. As the number of magnetic barriers increases, this range shrinks, the gaps in the transmission versus energy become wider, and the conductance oscillates with the Fermi energy.

Abstract: Graphene’s remarkable electronic properties have fuelled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor graphene’s electronic properties and to control its charge carriers. Here we show that a single-atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunnelling microscope. The response of the conduction electrons in graphene to the local charge is monitored with scanning tunnelling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states within a disc centred on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a mechanism to control and guide electrons in graphene.

Abstract: The properties of a new class of phosphorene nanotubes (PNT) are investigated by performing first-principles calculations. We demonstrate that it is advantageous to use blue phosphorene in order to make small nanotubes and propose a way to create low-energy PNTs by the inclusion of defect lines. Five different types of defect lines are investigated and incorporated in various combinations. The resulting defect-induced faceted PNTs have negligible bending stresses which leads to a reduction in the formation energy with respect to round PNTs. Our armchair faceted PNTs have similar formation energies than the recently proposed multiphase faceted PNTs, but they have a larger variety of possible structures. Our zigzag faceted PNTs have lower formation energies than round tubes and multiphase faceted nanotubes. The electronic properties of the defect-induced faceted PNTs are determined by the defect lines which control the band gap and the shape of the electronic states at the band edges. These band gaps increase with the radius of the nanotubes and converge to those of isolated defect lines.

Abstract: Piezoelectricity is a unique material property that allows one to convert mechanical energy into electrical one or vice versa. Transition metal dichalcogenides (TMDC) and transition metal dioxides (TMDO) are expected to have great potential for piezoelectric device applications due to their noncentrosymmetric and two-dimensional crystal structure. A detailed theoretical investigation of the piezoelectric stress (e 11 ) and piezoelectric strain (d 11 ) coefficients of single layer TMDCs and TMDOs with chemical formula MX 2 (where M= Cr, Mo, W, Ti, Zr, Hf, Sn and X = O, S, Se, Te) is presented by using first-principles calculations based on density func- tional theory. We predict that not only the Mo- and W-based members of this family but also the other materials with M= Cr, Ti, Zr and Sn exhibit highly promising piezoelectric properties. CrTe 2 has the largest e 11 and d 11 coefficients among the group VI elements (i.e., Cr, Mo, and W). In addition, the relaxed-ion e 11 and d 11 coefficients of SnS 2 are almost the same as those of CrTe 2 . Furthermore, TiO 2 and ZrO 2 pose comparable or even larger e 11 coefficients as compared to Mo- and W-based TMDCs and TMDOs. Our calculations reveal that TMDC and TMDO structures are strong candidates for future atomically thin piezoelectric applications such as transducers, sensors, and energy harvesting devices due to their piezoelectric coefficients that are comparable (even larger) to currently used bulk piezoelectric materials.

Abstract: Using the tight-binding approach, we study the influence of a perpendicular magnetic field on the energy levels of hexagonal, triangular, and circular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We obtain the energy levels for AB (Bernal)-stacked BLG QDs in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). We find different regions in the spectrum of biased QDs with respect to the crossing point between the lowest-electron and -hole Landau levels of a biased BLG sheet. Those different regions correspond to electron states that are localized at the center, edge, or corner of the BLG QD. Quantum Hall corner states are found to be absent in circular BLG QDs. The spatial symmetry of the carrier density distribution is related to the symmetry of the confinement potential, the position of zigzag edges, and the presence or absence of interlayer inversion symmetry.