In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter ν. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states.
In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value…
In this paper we investigate the relativistic quantum dynamics of a massive excitation in a graphene layer with a wedge disclination in the presence of an uniform magnetic field. We use a Dirac oscillator type coupling to introduce the confining potential for massive fermions in this system. We obtain the energy spectrum and eigenfunctions for the quantum ring pierced by Aharonov-Bohm flux resulting in appearance of persistent current and spontaneous magnetization.
In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed.
We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel f…
We investigate the wedge disclination effect on quantum tunneling of a Corbino disk in gapped-graphene of inner $R_1$ and outer $R_2$ radii in the presence of magnetic flux $Φ_i$. We solve Dirac equation for different regions and obtain the solutions of energy spectrum in terms of Hankel functions. The asymptotic behaviors for large arguments allow us to determine the transmission, Fano factor and conductance. We establish the case where the crystal symmetry is modified locally by replacing a hexagon by pentagon, square, heptagon or octagon. We show that the wedge disclination $n$ modifies the…
We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in the presence of a disclination. The calculations are performed in the continuum limit approximation in the vicinity of the Dirac points, solving Dirac equation by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearence of Aharonov-Bohm oscillation and find out the conditions of gapped and gapless states in the spectrum. We show that the gauge field due to a disclination lifts the orbital degeneracy originating from th…
Distributed Topological Charge and Spinorial Holonomy in Yukawa-Regularized Graphene Disclinations
Universidade Federal da Alagoas（阿拉戈斯联邦大学）；Universidade Estadual da Paraíba（帕拉伊巴州立大学）；Universidade Federal do Oeste da Bahia（巴伊亚西部联邦大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）
We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $γ=\pm 1$. We establish a correspondence between the bound state of (i) an isolated $Φ_0/2$-flux, (ii) an isolated pentagon $(n=1)$ or heptagon $(n=-1)$ defect with an external flux of magnitude $nγΦ_0/4$ through the center and (iii) an isolated square or octagon defect without external flux, where $Φ_0=h/e$ is the flux quantum. Due to the above correspondence, the existence of isolated electronic states bound to the disclinations is robust against…
The electronic structure in the vicinity of the 1-heptagonal and 1-pentagonal defects in the carbon graphene plane is investigated. Using a continuum gauge field-theory model the local density of states around the Fermi energy is calculated for both cases. In this model, the disclination is represented by an SO(2) gauge vortex and corresponding metric follows from the elasticity properties of the graphene membrane. To enhance the interval of energies, a self-consistent perturbation scheme is used. The Landau states are investigated and compared with the predicted values.
We construct an effective low energy Hamiltonian which describes fermions dwelling on a deformed honeycomb lattice with dislocations and disclinations, and with an arbitrary hopping parameters of the corresponding tight binding model. It describes the interaction of fermions with a 2d gravity and has also a local SU(2) gauge invariance of the group of rotations. We reformulate the model as interaction of fermions with the deformation of the lattice, which forms a phonon field. We calculate the response of fermion currents to the external deformation or phonon field, which is a result of a Z_2 …
We investigate the chemisorptions of oxygen molecules on bilayer graphene (BLG) and its electrically modified charge-doping effect using conductivity measurement of the field effect transistor channeled with BLG. We demonstrate that the change of the Fermi level by manipulating the gate electric field significantly affects not only the rate of molecular adsorption but also the carrier-scattering strength of adsorbed molecules. Exploration of the charge transfer kinetics reveals the electrochemical nature of the oxygen adsorption on BLG. [This document is the unedited Author's version of a Subm…
We consider the scattering of Dirac particles in graphene due to the superposition of an external magnetic field and mechanical strain. As a model for a graphene nanobubble, we find exact analytical solutions for single-particle states inside and outside a circular region submitted to the fields. Finally, we obtain analytical expressions for the scattering cross-section, as well as for the Landauer current through the circular region. Our results provide a fully-analytical treatment for electronic transport through a graphene nanobubble, showing that a combination of a physical magnetic field …
We consider a system of Dirac fermions in graphene submitted to a constant perpendicular magnetic field and scattered by a barrier potential. We show that our system can be used to establish a link with quantum optics through the Goos-Hänchen shifts. This can be done by evaluating the corresponding transmission probability and shift phase. We obtain Goos-Hänchen like shifts in terms of different physical parameters such as energy, electrostatic potential strength and magnetic field. On the light of this relation, we discuss the obtained results and make comparison with literature.
In a recent paper (JPCM 29, 445302 (2017)) we have studied the effects of mechanical strain and magnetic field on the electronic transport properties in graphene. In this article we extended our work to Weyl semimetals (WSM). We show that although the WSM are 3D materials, most of the analysis done for graphene (2D material) can be carried out. In concrete, we studied the an electronic transport through a cylindrical region submitted to torsional strain and external magnetic field. We provide exact analytical expressions for the scattering cross section and the transmitted electronic current. …
We have revealed the decisive role of grain-boundary-induced strain fields in electron scattering in polycrystalline graphene. To this end, we have formulated the model based on Boltzmann transport theory which properly takes into account the microscopic structure of grain boundaries (GB) as a repeated sequence of heptagon-pentagon pairs. The effect of strain field is described within the deformation potential theory. For comparison, we consider the scattering due to electrostatic potential of charged grain boundary. We show that at naturally low GB charges the deformation potential scattering…
Lattices with a basis can host crystallographic defects which share the same topological charge (e.g.~the Burgers vector $\vec b$ of a dislocation) but differ in their microscopic structure of the core. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, the microscopic details drastically affect the electronic structure: modifications can create or annihilate non-trivial bound states with an associated fractional charge. We show that this observation is related to the behavior of end modes of a dimerized chain and discuss how the end or defect…
We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through the Pauli--Schrödinger Hamiltonian H_{s}^{SP}. This will be helpful in the sense that the Dirac eigenvalues and eigenfunctions will be easily derived. In analyzing H_{s}^{SP} spectrum, we show that there is a composite fermion nature supported by the presence of two effective magnetic fields. For the lowest Landau level, we argue that the basic physics of grap…
