Coulomb impurity problem of graphene in magnetic fields

Analytical solutions to the Coulomb impurity problem of graphene in the absence of a magnetic field show that when the dimensionless strength of the Coulomb potential g$g$ reaches a critical value the solutions become supercritical with imaginary eigenenergies. Application of a magnetic field is a singular perturbation, and no analytical solutions are known except at a denumerably infinite set of magnetic fields. We find solutions to this problem by numerical diagonalization of the large Hamiltonian matrices. Solutions are qualitatively different from those of zero magnetic field. All energies are discrete and no complex energies are allowed. We have computed the finite-size scaling function of the probability density containing an s$s$-wave component of the Dirac wavefunctions. This function depends on the coupling constant, regularization parameter, and the gap. In the limit of vanishing regularization parameter our findings are consistent with the expected values of the exponent ν$\nu$ which determines the asymptotic behavior of the wavefunction near r=0$r=0$.     

Plasmon modes in 3-layer graphene structures: Inhomogeneity effects

We calculate the plasmon frequency and damping rate in a 3-layer graphene system made of parallel monolayer and bilayer graphene sheets using the random-phase-approximation dielectric function and taking into account the inhomogeneity of the dielectric background of the system. Numerical results show that two out-of-phase acoustic and one in-phase optical plasmon modes can be found from the zeroes of dynamical dielectric function of the structure. Plasmon frequencies and damping rate of plasma oscillations depend significantly on the inhomogeneity of environment, so plasmon curves become more distinctive from each other in single-particle excitation region, compared to the case of homogeneous medium. Finally, Plasmon dispersion patterns depend remarkably on the number (but not order) of bilayer graphene sheet constructing to the system.     

Angle-resolved photoemission spectroscopy studies of electron-electron interactions in graphene

Graphene is an emergent research topic that has attracted a huge amount of research interest ever since its experimental demonstration as a two-dimensional realization of Dirac fermions in 2005. In subsequent years, the research on graphene has rapidly expanded its field not only due to the new paradigm to study relativistic high energy physics in a condensed matter, but also due to its potential in the application for next generation devices. Most of the novel phenomena observed so far in graphene are attributed to its low-energy excitations, which is described by those of relativistic Dirac fermions. This article reviews recent progress in angle-resolved photoemission spectroscopy studies of electron-electron interactions in graphene.     

Splitting of the Fano resonance by Coulomb interactions in a two-dot quantum ring

We study the splitting of the Fano resonance in a Aharonov–Bohm interferometer with a quantum dot in each of its arms. Both intra- and inter-dot Coulomb repulsions are taken into account by employing the Keldysh nonequilibrium Green’s function technique. The single narrow Fano resonance in the noninteracting case is split into two in the presence of either intra- or inter-dot Coulomb interaction. We find that four Fano peaks emerge in the conductance or local density of states spectra when the two kinds of interactions exist simultaneously. Such behavior holds true for the accompanying broad Breit–Wigner type resonance. We also show that the positions of the Fano peaks can be tuned with the aid of the magnetic flux penetrating through the ring, which might have practical applications in device design or quantum computation.     

Bound states in disclinated graphene with Coulomb impurities in the presence of a uniform magnetic field

In this contribution, we study the effects caused by an impurity on the quantum dynamics of massive excitations in a disclinated graphene in the presence of an external magnetic field. Within a continuum approach, the problem is mathematically modeled by the definition of a special vector potential containing all the information about the topology and the interacting fields. The presence of disclination is introduced by a term in the Dirac equation that translates the appearance of a phase associated with the transport of the spinor around the apex of the cone. We solve exactly the Dirac equation for this problem and the eigenvalues are obtained. We observe the influence of the disclination on the spectrum of energy and the allowed values of magnetic field.     

Analytical expressions for electrostatics of graphene structures

This study focuses on electrostatics of various graphene structures as graphene monolayer, graphene nanoribbons, as well as multi-layer graphene or graphene flakes. An atomistic moment method based on classical electrostatics is utilized in order to evaluate the charge distribution in each nanostructure. Assuming a freestanding graphene structure in an infinite or in a semi-infinite space limited by a grounded infinite plane, the effect of the length, width, number of layers and position of the nanostructure on its electrostatic charge distributions and total charge and capacitance is examined through a parametric analysis. The results of the present show good agreement with corresponding available data in the literature, obtained from different theoretical approaches. Performing nonlinear regression analysis on the numerical results, where it is possible, simple analytical expressions are proposed for the total charge and charge distribution prediction based on structure geometry.     

Two-terminal quantized conductance in inhomogeneous graphene

Quantized two-terminal conductance plateaus in graphene were observed and were explained through the mechanism of different Landau level filling factors in inhomogeneous sample. Furthermore, the quantized conductance plateaus are different due to the difference of the carrier exchange through the graphene-substrate interface during the increasing and decreasing gate voltage-sweeps.     

Band structures of defective graphenes

Band structures of defective graphenes are analyzed by crystal orbital method. In laterally slipped faults, there appear σ bands consisting of weakly interacted dangling bonds. The peculiar σ bands cross with frontier π bands, and the resultant double occupation leads to the disappearance of ferromagnetic interactions. On the other hand, in longitudinally slipped faults, there are no crossings of the σ bands within the frontier levels, and the ferromagnetic interactions result from polycarbene-type spin alignment.     

Colossal enhancement in thermoelectric effect in a laterally coupled double-quantum-dot chain by the Coulomb interactions

Thermoelectric effects, including Seebeck coefficient (S), thermal conductance (κ), and figure of merit (ZT), in a laterally coupled double-quantum-dot (DQD) chain with two external nonmagnetic contacts are investigated theoretically by the nonequilibrium Green's function formalism. In this system, the DQD chain between two contacts forms a main channel for thermal electrons transporting, and each QD in the main chain couples laterally to a dangling one. The numerical calculations show that the Coulomb interactions not only lead to the splitting of the asymmetrical double-peak structure of the Seebeck coefficient, but also make the thermal spectrum show a strong violation of the Wiedemann–Franz law, leading to a colossal enhancement in ZT. These results indicate that the coupled DQD chain has potential applications in the thermoelectric devices with high thermal efficiency.     

Interfacial thermal resistance in multilayer graphene structures

The cross-plane thermal conductivities of multilayer graphene are investigated using nonequilibrium molecular dynamics simulation. It is found that the interfacial thermal resistance in multilayer graphene structures is strongly layer number dependent. It decreases with increasing layer number and reaches a limit as layer number is large enough. The interfacial thermal resistance for graphite and multilayer graphene has an anomalous relationship with temperature compared with that in superlattice structures. It increases with the temperatures above room temperature, which is attributed to phonon tunneling effects. Phonon tunneling probability is reduced due to the decreased phonon wavelength while temperature rises, which in turn causes the increased interfacial thermal resistance.     

Topological vortices in chiral gauge theory of graphene

Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently, Chamon, Jackiw et al. proposed a mechanism of using a Kekulé distortion background field φ and its induced gauge potential A_i to generate energy gaps. In this paper, various vortex structures inhering in this model are studied. Regarding φ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface—the velocity field vortices and the monopole-motion induced vortices—from the inner structure of the potential A_i. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.     

Exchange and Coulomb interactions of two electrons in double ellipsoidal quantum dots

The present study seeks to scrutinize the interactions of two electrons on the electronic properties of double ellipsoidal quantum dots (EQD). In this regard, the effective-mass approximation within a perturbation scheme is used and the Coulomb and exchange energies of the two electrons ellipsoidal quantum dot are calculated for GaAs/GaAlAs/AlAs structure. The results showed that the Coulomb and exchange energies depend not only on the thickness of the intermediate layer but also on the ellipticity constant.     

Spatial variation in the electronic structures of carpetlike graphene nanoribbons and sheets

Graphene, when deposited on a supporting substrate with a step edge, may be deformed in the presence of the step edges of the substrate. In this study, we have investigated a spatial variation in the local electronic structure near the step region, by performing first-principles calculations for carpetlike armchair graphene nanoribbons (C-AGNR) and two-dimensional periodic carpetlike graphene sheets (PCGS). Our results indicate no practical difference in the local density of states (LDOS) between those of flat and step regions. Interestingly, however, the PCGS shows a remarkable variation in the LDOS with an external electric field (E-field). Furthermore, we also discuss the dependence of the direction and the magnitude of the applied E-field on the spatial variation in the LDOS.     

Spectral self-similarity in fractal one-dimensional photonic structures

Transmission spectra of one-dimensional fractal multilayer structures are found to exhibit self-similar properties. Self-similarity manifests itself in the shape of a transmission envelope (map of transmission dips) rather than in the map of resonance transmission peaks, as is commonly the case with spectra of quasiperiodic systems. To observe the self-similarity, one needs to apply a power transformation to the transmittance in addition to the usual frequency scaling. The values of this power as well as the scaling factor have been calculated analytically and found to depend on the geometrical parameters of the structure.     

Spatial condensation of trapped polaritons in graphene and semiconductor structures

The theoretical and experimental status of the Bose–Einstein Condensation (BEC) of trapped quantum well (QW) polaritons in a microcavity is presented. The results of recent experiments that have shown the possibility to create an in-plane harmonic potential trap for a two-dimensional (2D) exciton polaritons in a cavity are discussed. We report the theory of BEC and of the trapped QW exciton polaritons in a microcavity. In addition, we study the BEC of trapped magnetoexciton polaritons in a graphene layer (GL) embedded in an optical microcavity in high magnetic field. In both cases the polaritons are considered to be in a harmonic potential trap. We compare the theoretical results with the existing experiments and discuss the experimental observation of predicted phenomena.     

Atomic and electronic structures of divacancy in graphene nanoribbons

First principles calculations have been performed to investigate the electronic structures and transport properties of defective graphene nanoribbons (GNRs) in the presence of pentagon-octagon-pentagon (5-8-5) defects. Electronic band structure results reveal that 5-8-5 defects in the defective zigzag graphene nanoribbon (ZGNR) is unfavorable for electronic transport. However, such defects in the defective armchair graphene nanoribbon (AGNR) give rise to smaller band gap than that in the pristine AGNR, and eventually results in semiconductor to metal-like transition. The distinct roles of 5-8-5 defects in two kinds of edged-GNR are attributed to the different coupling between π^? and π subbands influenced by the defects. Our findings indicate the possibility of a new route to improve the electronic transport properties of graphene nanoribbons via tailoring the atomic structures by ion irradiation.     

Wake effect in interactions of dipolar molecules with doped graphene

We study the wake effect in the charge carrier density in free graphene induced by an electric dipole moving parallel to it by using the dynamic polarization function of graphene within the random phase approximation for its π electrons described as Dirac?s fermions. We show that, while the equilibrium doping density of graphene sets a length scale for the period of the wake via graphene?s Fermi wavenumber, qualitative properties of the wake are strongly affected by the speed of the dipole, its distance from graphene, and the dipole moment orientation.     

Crossed Andreev reflection in graphene normal-superconductor-normal structures with pseudo-diffusive interfaces

In this Letter graphene normal-superconductor-normal heterostructures are modeled for studying the crossed Andreev reflection. A thin layer of undoped graphene with Fermi energy at the Dirac point at is assumed the interface between superconductor layer and each normal lead. The resulting contribution of the crossed Andreev reflection to the nonlocal conductance equals that of the electron elastic cotunneling. We explain this as another figure of merit for pseudodiffusive conduction at the Dirac point of the undoped layers. Also structures with only one undoped layer at the interface between the superconductor and one of the normal leads, as well as structures in which one of the leads is ferromagnetic, show pseudodiffusive conduction at the Dirac points.