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Recent experimental measurements of light absorption in few-layer black phosphorus (BP) reveal 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 black phosphorus (BP) within a continuum approach for the in-plane degrees of freedom and a tight-binding approximation that accounts for inter-layer couplings. This yields excitonic transitions between different combinations of the sub-bands 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 sub-band 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., Comment: to appear in Phys. Rev. B

The effect of an external in-plane electric field on neutral and charged exciton states in two-dimensional (2D) materials is theoretically investigated. These states are argued to be strongly bound, so that electron-hole dissociation is not observed up to high electric field intensities. Trions in the anisotropic case of monolayer phosphorene are demonstrated to especially robust under electric fields, so that fields as high as 100 kV/cm yield no significant effect on the trion binding energy or probability density distribution. Polarizabilities of excitons are obtained from the parabolicity of numerically calculated Stark shifts. For trions, a fourth order Stark shift is observed, which enables the experimental verification of hyperpolarizability in 2D materials, as observed in the highly excited states of the Rydberg series of atoms and ions., Comment: 7 pages, 4 figures, 3 tables

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., Comment: 14 pages, 8 figures

We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change of sign in the group velocity. Second, a surface plasmon-magnon polariton formed as a linear superposition of graphene surface plasmon and the antiferromagnetic bare magnon. This polariton has a dispersion with two branches, formed by the anticrossing between the dispersive surface plasmon and the magnon. We discuss the potential these new modes have for combining photons, magnons, and plasmons to reach new functionalities., Comment: 12 pages, 4 figures

We study the addition energy spectra of phosphorene quantum dots focusing on the role of dot size, edges passivation, number of layers and dielectric constant of the substrate where the dots are deposited. We show that for sufficiently low dielectric constants ($\varepsilon_{sub} < 4$), Coulomb blockade can be observed in dot sizes larger than 10 nm, for both passivated and unpassivated edges. For higher dielectric constants (up to $\varepsilon_{sub} = 30$), Coulomb blockade demands smaller dot sizes, but this depends whether the edges are passivated or not. This dramatic role played by the substrate is expected to impact on the development of application based on phosphorene quantum dots.

Dielectric screening is greatly important to an accurate calculation of the exciton binding energies in two-dimensional materials. In this work, we calculate the dielectric function and 2D polarizability of multilayer (up to three) phosphorene sheets using Density Functional Theory. The 2D polarizabilities are then used in the dielectric screening of the excitonic interaction in multilayer phosphorene quantum dots. In the limit of large quantum dots, excitonic gaps are shown to exhibit very good agreement with state-of-the-art measurements of the optical gaps of multilayer phosphorene sheets deposited in different substrates.

We study the size-dependent exciton fine structure in monolayer black phosphorus quantum dots (BPQDs) deposited on different substrates (isolated, Si and SiO$_2$) using a combination of tight-binding method to calculate the single-particle states, and the configuration interaction formalism to determine the excitonic spectrum. We demonstrate that the substrate plays a dramatic role on the excitonic gaps and excitonic spectrum of the QDs. For reasonably high dielectric constants ($\varepsilon_{sub} \sim \varepsilon_{Si} = 11.7 \varepsilon_0$), the excitonic gap can be described by a single power law $E_X(R) = E_X^{(bulk)} + C/R^{\gamma}$. For low dielectric constants $\varepsilon_{sub} \leq \varepsilon_{SiO_2} = 3.9 \varepsilon_0$, the size dependence of the excitonic gaps requires the sum of two power laws $E_X(R) = E_g^{(bulk)} + A/ R^{n} - B/R^{m}$ to describe both strong and weak quantum confinement regimes, where $A$, $B$, $C$, $\gamma$, $n$, and $m$ are substrate-dependent parameters. We also predict that the exciton lifetimes exhibit a strong temperature dependence, ranging between 2-8 ns (Si substrate) and 3-11 ns (SiO$_2$ substrate) for QDs up 10 nm in size.

We theoretically study a current switch that exploits the phase acquired by a charge carrier as it tunnels through a potential barrier in graphene. The system acts as an interferometer based on an armchair graphene quantum ring, where the phase difference between interfering electronic wave functions for each path can be controlled by tuning either the height or the width of a potential barrier in the ring arms. By varying the parameters of the potential barriers the interference can become completely destructive. We demonstrate how this interference effect can be used for developing a simple graphene-based logic gate with high on/off ratio, Comment: 6 pages, 6 figures

We present a theoretical study of the charging effects in single and double layer black phosphorus quantum dots (BPQDs) with lateral sizes of 2 nm and 3 nm. We demonstrate that the charging of BPQDs are able to store up to an $N_{max}$ electron (that depends on the lateral size and number of layers in the QD), after which structural instabilities arises. For example, 3 nm wide hydrogen-passivated single layer BPQDs can hold a maximum of 16 electrons, and an additional electron causes the expelling of hydrogen atoms from the QD borders. We also calculated the additional energy ($E_A$) spectrum. For single layer QDs with 2 and 3 nm of lateral sizes, the average $E_A$ is around 0.4 eV and 0.3 eV, respectively. For double layer QDs with the same sizes, the average $E_A$ is around 0.25 eV and 0.2 eV, respectively.

A pseudo-magnetic 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 pseudo-magnetic 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., Comment: 8 pages, 6 figures

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., Comment: 7 pages, 6 figures

The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger 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., Comment: 19 pages, 4 figures

We investigate the scattering of a wave packet describing low-energy electrons in graphene by a time-dependent finite step potential barrier. Our results demonstrate that, after Klein tunneling through the barrier, the electron acquires an extra energy which depends on the rate of change the barrier height in time. If such a rate is negative, the electron loses energy and ends up as a valence band state after leaving the barrier, which effectively behaves as a positively charged quasi-particle, Comment: 5 pages, 5 figures, Fig. 3 selected for the Kaleidoscope section (Sept. 2015) of Phys. Rev. B

We numerically study the vortex-vortex interaction in multi-component homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidences that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and inter-component vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multi-component Bose-Einstein condensates, and the understanding of the role of vortex interactions in multiband superconductors., Comment: Published in PRA

In this work we investigate electron-impurity binding energy in GaN/HfO$_2$ quantum wells. The calculation considers simultaneously all energy contributions caused by the dielectric mismatch: (i) image self-energy (i.e., interaction between electron and its image charge), (ii) the direct Coulomb interaction between the electron-impurity and (iii) the interactions among electron and impurity image charges. The theoretical model account for the solution of the time-dependent Schr\"odinger equation and the results shows how the magnitude of the electron-impurity binding energy depends on the position of impurity in the well-barrier system. The role of the large dielectric constant in the barrier region is exposed with the comparison of the results for GaN/HfO$_2$ with those of a more typical GaN/AlN system, for two different confinement regimes: narrow and wide quantum wells., Comment: 6 Pages, 7 figures

We report numerical results which show the achievement of net transport of self-propelled particles (SPP) in the presence of a two-dimensional regular array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive inter-particle (soft disks) and particle-obstacle interactions present no alignment rule. We find that SPP 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 SPP around the obstacles. An steady particle current is spontaneously established in an array of non-symmetric convex obstacle (which presents no cavity in which particles may be trapped in), 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., Comment: 5 pages, 3 figuras, accepted for publication in Phys. Rev. E

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 Schrodinger 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, specially in the presence of external magnetic fields, and lead to drastic modifications in the oscillator strength., Comment: 17 pages, 10 figures

We theoretically demonstrate that the transport inefficiency recently found experimentally for branched-out mesoscopic networks can also be observed in a quantum ring of finite width with an attached central horizontal branch. This is done by investigating the time evolution of an electron wave packet in such a system. Our numerical results show that the conductivity of the ring does not necessary improves if one adds an extra channel. This ensures that there exists a quantum analogue of the Braess Paradox, originating from quantum scattering and interference., Comment: accepted for publication in Phys. Rev. B

This work presents a theoretical study of the energy spectrum of GaAs/AlGaAs concentric double quantum rings, under an applied magnetic field directed perpendicular to the ring plane. The Schrodinger equation for this system is solved in a realistic model consisting of rings with finite barrier potentials. Numerical results show that increasing the magnetic field intensity leads to oscillations in the ground state energy which, in contrast to the usual Aharonov-Bohm oscillations, do not have a well defined period, due to the coupling between inner and outer rings states. However, when one considers an elliptical geometry for the rings, the energy spectra of the inner and outer ring states are decoupled and the periodicity of the oscillations is recovered.

We investigate the excitonic properties of a core-multishell semiconductor nanowire with type-II band mismatch, i.e. with spatially separated electrons and holes, under an external magnetic field. Our results demonstrate that, depending on the core wire radius, the carrier in the type-II band exhibits either a quantum dot-like or a quantum ring-like energy spectrum, corresponding to a carrier confinement in the core wire or in the outer shell, respectively. In the latter, a shell-to-core confinement transition can be induced by increasing the magnetic field intensity, which may lead to interesting photocurrent properties of these confining structures, tunable by the external field.

We investigate the magnetic interface states of graphene quantum dots that contain p-n junctions. Within a tight-binding approach, we consider rectangular quantum dots in the presence of a perpendicular magnetic field containing p-n, as well as p-n-p and n-p-n junctions. The results show the interplay between the edge states associated with the zigzag terminations of the sample and the snake states that arise at the p-n junction, due to the overlap between electron and hole states at the potential interface. Remarkable localized states are found at the crossing of the p-n junction with the zigzag edge having a dumb-bell shaped electron distribution. The results are presented as function of the junction parameters and the applied magnetic flux., Comment: 13 pages, 23 figures, to be appeared in Phys. Rev. B

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., Comment: 9 pages, 13 figures, to appear in Phys. Rev. E (2013)

The scattering of a Gaussian wavepacket in armchair and zigzag graphene edges is theoretically investigated by numerically solving the time dependent Schr\"odinger equation for the tight-binding model Hamiltonian. Our theory allows to investigate scattering in reciprocal space, and depending on the type of graphene edge we observe scattering within the same valley, or between different valleys. In the presence of an external magnetic field, the well know skipping orbits are observed. However, our results demonstrate that in the case of a pseudo-magnetic field, induced by non-uniform strain, the scattering by an armchair edge results in a non-propagating edge state., Comment: 8 pages, 7 figures

We theoretically investigate the role of the dielectric mismatch between materials on the energy levels and recombination energies of a core-shell nanowire. Our results demonstrate that when the dielectric constant of the core material is lower than that of the shell material, the self-image potential pushes the charge carriers towards the core-shell interface, in such a way that the ideal confinement model is no longer suitable. The effects of this interfacial confinement on the electronic properties of such wires, as well as on its response to applied magnetic fields, are discussed., Comment: 4 pages, 3 figures and 1 material Supplementary; Applied Physics Letters 2012

The electronic band structure of cubic HfO2 is calculated using an it ab initio all-electron self--consistent linear augmented plane-wave method, within the framework of the local-density approximation and taking into account full-relativistic contributions. From the band structure, the carrier effective masses and the complex dielectric function are obtained. The \Gamma-isotropic heavy and light electron effective masses are shown to be several times heavier than the electron tunneling effective mass measured recently. The imaginary part of the complex dielectric function \epsilon_2(\omega) is in good agreement with experimental data from ultraviolet spectroscopic ellipsometry measurements in bulk yttria-stabilized HfO2 as well as with those performed in films deposited with the tetrakis diethylamido hafnium precursor for energies smaller than 9.5 eV.

Structural, electronic, and optical properties for the cubic, tetragonal, and monoclinic crystalline phases of ZrO2, as derived from it ab initio full-relativistic calculations, are presented. The electronic structure calculations were carried out by means of the all-electron full potential linear augmented plane wave method, within the framework of the density functional theory and the local density approximation. The calculated carrier effective masses are shown to be highly anisotropic. The results obtained for the real and imaginary parts of the dielectric function, the reflectivity, and the refraction index, show good agreement with the available experimental results. In order to obtain the static dielectric constant of ZrO2, we added to the electronic part, the optical phonons contribution, which leads to values of e1(0)~29.5, 26.2, 21.9, respectively along the xx, yy, and zz directions, for the monoclinic phase, in excellent accordance with experiment. Relativistic effects, including the spin-orbit interaction, are demonstrated to be important for a better evaluation of the effective mass values, and in the detailed structure of the frequency dependent complex dielectric function.

The electronic band structures and optical properties of cubic, tetragonal, and monoclinic phases of HfO2 are calculated using the first-principles linear augmented plane-wave method, within the density functional theory and generalized gradient approximation, and taking into account full-relativistic contributions. From the band structures, the electron- and hole-effective masses were obtained. Relativistic effects play an important role, which is reflected in the effective masses values and in the detailed structure of the dielectric function. The calculated imaginary part of the dielectric function and refractive index are in good agreement with the data reported in the literature.

The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single particle energy levels are calculated as function of an external perpendicular magnetic field which lifts degeneracies. Comparing the energy spectra obtained from the tight-binding approximation to those obtained from the continuum Dirac equation approach, we verify that the behavior of the energies as function of the dot size or the applied magnetic field are qualitatively similar, but in some cases quantitative differences can exist., Comment: 13 pages, 18 figures. To be appeared in Phys. Rev. B

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for $\hat x$ and $\hat p_\gamma$. Such a formalism naturally leads to a Schr\"odinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach is demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers., Comment: 5 pages, 4 figures

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 layer of BLG. We found that: i) due to the strong confinement by the single kink profile the uni-directional 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 anti-crossing points in the energy spectrum. This leads to the opening of tunable minigaps in the spectrum of the uni-directional topological states., Comment: To appear in Phys. Rev. B

The electronic spectrum of three coupled graphene layers (graphene trilayers) is investigated in the presence of an external magnetic field. We obtain analytical expressions for the Landau level spectrum for both the ABA and ABC - type of stacking, which exhibit very different dependence on the magnetic field. The effect of layer asymmetry and of external gate voltages can strongly influence the properties of the system., Comment: 8 pages, 9 figures. Submitted to Phys. Rev. B

We describe a semi-analytic approach to the two-band Ginzburg-Landau theory, which predicts the behavior of vortices in two-band superconductors. We show that the character of the short-range vortex-vortex interaction is determined by the sign of the normal domain - superconductor interface energy, in analogy with the conventional differentiation between type-I and type-II superconductors. However, we also show that the long-range interaction is determined by a modified Ginzburg-Landau parameter $\kappa^*$, different from the standard $\kappa$ of a bulk superconductor. This opens the possibility for non-monotonic vortex-vortex interaction, which is temperature-dependent, and can be further tuned by alterations of the material on the microscopic scale.

The time evolution of a wavepacket 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 pseudo-magnetic 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., Comment: 13 pages, 10 figures

The role of graded interfaces between materials in a cylindrical free-standing quantum wire with longitudinal heterostructures is theoretically investigated, by solving the Schr\"odinger equation within the effective mass approximation. Previous work on such wires with abrupt interfaces have predicted that, as the wire radius is reduced, the effective potential along the growth direction is altered and might lead to a carrier confinement at the barriers, as in a type-II system. Our results show that when graded interfaces are considered, such potential acquires a peculiar form, which presents cusps at the interfacial regions, yielding to electron confinement at interfaces. Numerical results also show that, in some special cases, interfacial confinement and type-I to type-II transitions can also be induced by applying a magnetic field parallel to the wire axis., Comment: 8 pages, 6 figures

Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) 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 (SFD) to the two-dimensional diffusion regime is investigated. This transition (regarding the calculation of the scaling exponent ($\alpha$) of the MSD $<\Delta x^{2}(t)>$ $\propto t^{\alpha}$) 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/stepwise (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., Comment: 13 pages, 11 figures

We consider a classical system of two-dimensional (2D) charged particles, which interact through a repulsive Yukawa potential $exp(-r/\lambda)/r$, confined in a parabolic channel which limits the motion of the particles in the $y$-direction. Along the $x$-direction, the particles are also subject to a periodic potential substrate. The ground state configurations and the normal mode spectra of the system are obtained as function of the periodicity and strength of the periodic potential ($V_0$), and density. An interesting set of tunable ground state configurations are found, with first and second order structural transitions between them. A magic configuration with particles aligned in each minimum of the periodic potential is obtained for V_0 larger than some critical value which has a power law dependence on the density. The phonon spectrum of different configurations were also calculated. A localization of the modes into a small frequency interval is observed for a sufficient strength of the periodic potential. A tunable band-gap is found as a function of $V_0$. This model system can be viewed as a generalization of the Frenkel and Kontorova model., Comment: Submmited to PRB

The ground state configurations and the \lq{}\lq{}normal\rq{}\rq{} mode spectra of a $quasi$-one-dimensional (Q1D) binary system of charged particles interacting through a screened Coulomb potential are presented. The minimum energy configurations were obtained analytically and independently through molecular dynamic simulations. A rich variety of ordered structures were found as a function of the screening parameter, the particle density, and the ratio between the charges of the distinct types of particles. Continuous and discontinuous structural transitions, as well as an unexpected symmetry breaking in the charge distribution are observed when the density of the system is changed. For near equal charges we found a disordered phase where a mixing of the two types of particles occurs. The phonon dispersion curves were calculated within the harmonic approximation for the one- and two-chain structures., Comment: 11 pages, 11 figs

The melting of a binary system of charged particles confined in a {\it 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 types 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 types of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct types of charges is observed., Comment: To appear in Journal of Physics: condensed matter ; (13 pages, 12 figures)

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 non-linear 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 inter-vortex separations which are available in the literature. We propose new empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter.

We demonstrate the existence of localized electron and hole states in a ring-shaped potential kink in biased bilayer graphene. Within the continuum description, we show that for sharp potential steps the Dirac equation describing carrier states close to the K (or K') point of the first Brillouin zone can be solved analytically for a circular kink/anti-kink dot. The solutions exhibit interfacial states which exhibit Aharonov-Bohm oscillations as functions of the height of the potential step and/or the radius of the ring.

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 non-zero gap in the spectrum. Our minimal model gives insight in the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings., Comment: To appear in Phys. Rev. B

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 $B_0 \to -B_0$ 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 anti-crossings, which arise due to the overlap of gate-confined and magnetically-confined states., Comment: 5 pages, 6 figures, to appear in Nano Letters