Effect of zitterbewegung on the propagation of wave packets in ABC-stacked multilayer graphene: an analytical and computational approach.

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.

Gap opening in graphene nanoribbons by application of simple shear strain and in-plane electric field.

The effects of shear strain and applied in plane electric field on the electronic properties of monolayer graphene nanoribbons (GNRs) are theoretically investigated. Band structures and the probability densities are calculated within the tight-binding model and the mechanical stresses submitted to the GNRs are taken into account by using the theory of linear elasticity with joint modifications in the elongation of the nearest-neighbor vectors and the modification of the hopping parameters. The energy gaps for specific widths of (semiconducting) armchair nanoribbons are verified also in the presence of either strain or field, whereas zigzag nanoribbons are metallic for any value of strain and exhibit a small gap for any value of field. However, our results demonstrate that when both strain and electric field are combined, a significant energy gap is always observed in the band structure, for any width or edge type of the ribbon. Moreover, the obtained total wave function is asymmetric along the ribbon width due to the applied electric field that pushes the electrons to one side of the ribbon and, under shear strain, a peak at the center of the ribbon in the spatial distribution is also observed owing to the preferable localization around the almost undeformed carbon bonds at ribbon center.

Magnetic field induced vortices in graphene quantum dots.

The energy spectrum and local current patterns in graphene quantum dots (QD) are investigated for different geometries in the presence of an external perpendicular magnetic field. Our results demonstrate that, for specific geometries and edge configurations, the QD exhibits vortex and anti-vortex patterns in the local current density, in close analogy to the vortex patterns observed in the probability density current of semiconductor QD, as well as in the order parameter of mesoscopic superconductors.

Structure and reentrant percolation in an inverse patchy colloidal system.

Two-dimensional systems of inverse patchy colloids modeled as disks with a central charge and having their surface decorated with oppositely pointlike charged patches are investigated using molecular dynamics simulations. The self-assembly of the patchy colloids leads to diverse ground state configurations ranging from crystalline arrangements of monomers to linear clusters, ramified linear clusters and to percolated configurations. Two structural phase diagrams are constructed: (1) as a function of the net charge and area fraction, and (2) as a function of the net charge and the range of the pair interaction potential. An interesting reentrant percolation transition is obtained as a function of the net charge of the colloids. We identify distinct mechanisms that lead to the percolation transition.

Valley filtering in graphene due to substrate-induced mass potential.

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 Schrödinger 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.

Electronic properties of superlattices on quantum rings.

We present a theoretical study of the one-electron states of a semiconductor-made quantum ring (QR) containing a series of piecewise-constant wells and barriers distributed along the ring circumference. The single quantum well and the superlattice cases are considered in detail. We also investigate how such confining potentials affect the Aharonov-Bohm like oscillations of the energy spectrum and current in the presence of a magnetic field. The model is simple enough so as to allow obtaining various analytical or quasi-analytical results. We show that the well-in-a-ring structure presents enhanced localization features, as well as specific geometrical resonances in its above-barrier spectrum. We stress that the superlattice-in-a-ring structure allows giving a physical meaning to the often used but usually artificial Born-von-Karman periodic conditions, and discuss in detail the formation of energy minibands and minigaps for the circumferential motion, as well as several properties of the superlattice eigenstates in the presence of the magnetic field. We obtain that the Aharonov-Bohm oscillations of below-barrier miniband states are reinforced, owing to the important tunnel coupling between neighbour wells of the superlattice, which permits the electron to move in the ring. Additionally, we analysis a superlattice-like structure made of a regular distribution of ionized impurities placed around the QR, a system that may implement the superlattice in a ring idea. Finally, we consider several random disorder models, in order to study roughness disorder and to tackle the robustness of some results against deviations from the ideally nanostructured ring system.

Electronic confinement in graphene quantum rings due to substrate-induced mass radial kink.

We investigate localized states of a quantum ring confinement in monolayer graphene defined by a circular mass-related potential, which can be induced e.g. by interaction with a substrate that breaks the sublattice symmetry, where a circular line defect provides a change in the sign of the induced mass term along the radial direction. Electronic properties are calculated analytically within the Dirac-Weyl approximation in the presence of an external magnetic field. Analytical results are also compared with those obtained by the tight-binding approach. Regardless of its sign, a mass term [Formula: see text] is expected to open a gap for low-energy electrons in Dirac cones in graphene. Both approaches confirm the existence of confined states with energies inside the gap, even when the width of the kink modelling the mass sign transition is infinitely thin. We observe that such energy levels are inversely proportional to the defect line ring radius and independent on the mass kink height. An external magnetic field is demonstrated to lift the valley degeneracy in this system and easily tune the valley index of the ground state in this system, which can be polarized on either K or [Formula: see text] valleys of the Brillouin zone, depending on the magnetic field intensity. Geometrical changes in the defect line shape are considered by assuming an elliptic line with different eccentricities. Our results suggest that any defect line that is closed in a loop, with any geometry, would produce the same qualitative results as the circular ones, as a manifestation of the topologically protected nature of the ring-like states investigated here.

Self-propelled particle transport in regular arrays of rigid asymmetric obstacles.

We report numerical results which show the achievement of net transport of self-propelled particles (SPPs) in the presence of a two-dimensional regular array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive interparticle (soft disks) and particle-obstacle interactions present no alignment rule. We find that SPPs present a vortex-type motion around convex symmetric obstacles even in the absence of hydrodynamic effects. Such a motion is not observed for a single SPP, but is a consequence of the collective motion of SPPs around the obstacles. A steady particle current is spontaneously established in an array of nonsymmetric convex obstacles (which presents no cavity in which particles may be trapped), and in the absence of an external field. Our results are mainly a consequence of the tendency of the self-propelled particles to attach to solid surfaces.

Electric and magnetic field effects on the excitonic properties of elliptic core-multishell quantum wires.

The effect of eccentricity distortions of core-multishell quantum wires on their electron, hole and exciton states is theoretically investigated. Within the effective mass approximation, the Schrödinger equation is numerically solved for electrons and holes in systems with single and double radial heterostructures, and the exciton binding energy is calculated by means of a variational approach. We show that the energy spectrum of a core-multishell heterostructure with eccentricity distortions, as well as its magnetic field dependence, are very sensitive to the direction of an externally applied electric field, an effect that can be used to identify the eccentricity of the system. For a double heterostructure, the eccentricities of the inner and outer shells play an important role on the excitonic binding energy, especially in the presence of external magnetic fields, and lead to drastic modifications in the oscillator strength.

Conductance maps of quantum rings due to a local potential perturbation.

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 ϕ0 periodic Aharonov-Bohm oscillation pattern into a ϕ0/2 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 conductance map.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel.

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

Bilayer crystals of charged magnetic dipoles: structure and phonon spectrum.

We study the structure and phonon spectrum of a two-dimensional bilayer system of classical charged dipoles oriented perpendicular to the plane of the layers for equal density in each layer. This system can be tuned through six different crystalline phases by changing the interlayer separation or the charge and/or dipole moment of the particle. The presence of the charge on the dipole particles is responsible for the nucleation of five staggered phases and a disordered phase which are not found in the magnetic dipole bilayer system. These extra phases are a consequence of the competition between the repulsive Coulomb and the attractive dipole interlayer interaction. We present the phase diagram and determine the order of the phase transitions. The phonon spectrum of the system was calculated within the harmonic approximation, and a nonmonotonic behavior of the phonon spectrum is found as a function of the effective strength of the interparticle interaction. The stability of the different phases is determined.

The electronic properties of graphene and graphene ribbons under simple shear strain.

A tight-binding model is used to study the energy band of graphene and graphene ribbon under simple shear strain. The ribbon consists of lines of carbon atoms in an armchair or zigzag orientation where a simple shear strain is applied in the x-direction keeping the atomic distances in the y-direction unchanged. Such modification in the lattice gives an energy band that differs in several aspects from the one without any shear and with pure shear. The changes in the spectrum depend on the line displacement of the ribbon, and also on the modified hopping parameter. It is also shown that this simple shear strain tunes the electronic properties of both graphene and graphene ribbon, opening and closing energy gaps for different displacements of the system. The modified density of states is also shown.

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel.

Diffusive properties of a monodisperse system of interacting particles confined to a quasi-one-dimensional channel are studied using molecular dynamics simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion to the two-dimensional diffusion regime is investigated. This transition [regarding the calculation of the scaling exponent (α) of the MSD (Δx(2)(t) ∝ t(α)] as a function of the width of the channel is shown to change depending on the channel's confinement profile. In particular, the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.

Diffusion in a quasi-one-dimensional system on a periodic substrate.

The diffusion of charged particles interacting through a repulsive Yukawa potential, exp(-r/λ)/r, confined by a parabolic potential in the y direction and subjected to a periodic substrate potential in the x direction is investigated. Langevin dynamic simulations are used to investigate the effect of the particle density, the amplitude of the periodic substrate, and the range of the interparticle interaction potential on the diffusive behavior of the particles. We found that in general the diffusion is suppressed with increasing the amplitude of the periodic potential, but for specific values of the strength of the substrate potential a remarkable increase of the diffusion is found with increasing the periodic potential amplitude. In addition, we found a strong dependence of the diffusion on the specific arrangement of the particles, e.g., single-chain versus multichain configuration. For certain particle configurations, a reentrant behavior of the diffusion is found as a function of the substrate strength due to structural transitions in the ordering of the particles.

Wavepacket scattering of Dirac and Schrödinger particles on potential and magnetic barriers.

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.

Fractal spectrum of charge carriers in quasiperiodic graphene structures.

In this work we investigate the interaction of charge carriers in graphene with a series of p-n-p junctions arranged according to a deterministic quasiperiodic substitutional Fibonacci sequence. The junctions create a potential landscape with quantum wells and barriers of different widths, allowing the existence of quasi-confined states. Spectra of quasi-confined states are calculated for several generations of the Fibonacci sequence as a function of the wavevector component parallel to the barrier interfaces. The results show that, as the Fibonacci generation is increased, the dispersion branches form energy bands distributed as a Cantor-like set. Besides, for a quasiperiodic set of potential barriers, we obtain the electronic tunneling probability as a function of energy, which shows a striking self-similar behavior for different generation numbers.

A two-component mixture of charged particles confined in a channel: melting.

The melting of a binary system of charged particles confined in a quasi-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different kinds of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four-chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two kinds of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct kinds of charges is observed.

Electrostatically confined quantum rings in bilayer graphene.

We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene. These structures can be created by tuning the gap of the graphene bilayer using nanostructured gates or by position-dependent doping. The energy levels have a magnetic field (B(0)) dependence that is strikingly distinct from that of usual semiconductor quantum rings. In particular, the eigenvalues are not invariant under a B(0) --> -B(0) transformation and, for a fixed total angular momentum index m, their field dependence is not parabolic, but displays two minima separated by a saddle point. The spectra also display several anticrossings, which arise due to the overlap of gate-confined and magnetically confined states.

Ground state and normal-mode spectra of a two-dimensional system of dipole particles confined in a parabolic trap.

The ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures like chains and Y-shaped configurations when a magnetic field is applied parallel to the plane of the particles. The normal-mode spectrum of the particles and its dependence on the magnetic field and the strength of the dipole moment of the particles are studied. The vibrational and rotational modes of the spectrum, which are associated with the stability of the system, are investigated in detail. The number of particles is varied and we found different ordering of the particles for different values of the dipole moment and the magnetic field. A ring structure with a large number of particles is observed for high values of the dipole moment of the particles.