Tunable electronic transmission gaps in a graphene superlattice

The transmission in graphene superlattices with adjustable barrier height is investigated using transfer-matrix method. It is found that one could control the angular range of transmission by changing the ratio of incidence energy and barrier height. The transmission as a function of incidence energy has more than one gaps, due to the appearance of evanescent waves in different barriers. Accordingly, more than one conductivity minimums are induced. The transmission gaps could be controlled by adjusting the incidence angle, the barrier height, and the barrier number, which gives the possibility to construct an energy-dependent wavevector filter.     

Topological mass generation four-dimensional gauge theory

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang–Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes massive Yang–Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high-rank tensor bosons.     

Helical states around a mass-inverted quantum dot in graphene

Topologically protected helical states at a mass-inverted quantum dot in graphene are studied by analyzing both tight-binding and kernel polynomial method calculations. The mass-inverted quantum dot is introduced by considering a heterojunction between two different mass domains, which is similar to the domain wall in bilayer graphene. The numerical results show emergent metallic channels across the mass gap when the signs of the mass terms are opposite. The eigenstates of the metallic channels are revealed to be doubly degenerate—each state propagates along opposite directions, maintaining the time-reversal symmetry of graphene. The robustness of the metallic channels is further examined, concluding with the fact that helical states are secured unless atomic vacancies form near the domain wall. Such helical states circulating along the topological defects may pave a novel route to engineering topological states based on graphene.     

Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Scattering of charge carriers in graphene induced by topological defects

We study the scattering of graphene quasiparticles by topological defects, represented by holes, pentagons and heptagons. For holes, we found that at low concentration they give a negligible contribution to the resistivity. Whenever pentagons or heptagons are introduced we realize that a fermionic current is scattered by defects.     

A Topological Glass

We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with n nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with other numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal of two adjacent triangles, with a temperature dependent probability. We show that this system has an approach to a steady state which is exponentially slow, and show that the stationary state is unordered. We also study the local energy landscape and show that it has the hierarchical structure known from spin glasses. Finally, we show that the evolution can be described as that of a rarefied gas with spontaneous generation of particles and annihilating collisions.     

Composite optical vortices in two noncollinear cosh-Gaussian vortex beams and their propagation properties in free space

The composite optical vortices (OVs) formed by superimposing two parallel, noncollinear cosh-Gaussian (ChG) vortex beams at the waist plane and their propagation in free space are studied. The dependence of the number, position and net topological charge of composite OVs on the control parameter, such as the relative phase, amplitude ratio, waist-width ratio, relative off-axis distance and decentered parameter, and on the propagation distance is illustrated numerically. A comparison with the previous work is also made.     

Effective mass and band gap of strained graphene

The effective mass of strained graphene is investigated by tight-binding and density-functional theory calculations. For graphene strained in the zigzag direction, we find a strong anisotropy in the effective mass near the gap opening, with an abrupt increase of the effective mass at the critical strain in one direction and a smooth variation perpendicular to it. There is no band-gap opening for isotropic strain, but at an expansive strain of about 28%, the lower edge of the s-band reaches the Fermi level and makes the graphene metallic.     

Commutator of gauge generators in non-abelian chiral theory

Commutators among non-abelian fermion currents are calculated using the BJL limit. The relation between the covariant seagull and the gauge dependence of the fermion current is derived for a canonical non-abelian theory using the path integral formulation. We observe that in a non-abelian theory with coupling to chiral fermions this relation is violated and this produces a non-trivial commutator of gauge group generators.     

Rb吸附石墨烯纳米带电子性质和光学性质的研究

本文基于密度泛函理论的第一性原理方法了计算了Rb、O和H吸附石墨烯纳米带的差分电荷密度、能带结构、分波态密度和介电函数,调制了石墨烯纳米带的电子性质和光学性质,给出了不同杂质影响材料光学特性的规律.结果表明本征石墨烯纳米带为n型直接带隙半导体且带隙值为0.639 eV;Rb原子吸附石墨烯纳米带之后变为n型简并直接带隙半导体,带隙值为0.494eV;Rb和O吸附石墨烯纳米带变为p型简并直接带隙半导体,带隙值增加为0.996eV;增加H吸附石墨烯纳米带后,半导体类型变为n型直接带隙半导体,且带隙变为0.299eV,带隙值相对减小,更有利于半导体发光器件制备.吸附Rb、O和H原子后,石墨烯纳米带中电荷密度发生转移,导致C、Rb、O和H之间成键作用显著.吸附Rb之后,在费米能级附近由C-2p、Rb-5s贡献;增加O原子吸附之后,O-2p在费米能级附近贡献非常活跃,杂化效应使费米能级分裂出一条能带;再增加H原子吸附之后,Rb-4p贡献发生蓝移,O-2p在费米能级附近贡献非常强,费米能级分裂出两条能带.Rb、O和H的吸附后,明显调制了石墨烯纳米带的光学性质.     

Topological textures and their bifurcation processes in 2D ferromagnetic thin films

In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from the viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex–antivortex pairs taking place at space–time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex core reversal are discussed in detail.     

Topological gravity from a transgression gauge field theory

It is shown that a topological action for gravity in even dimensions can be obtained from a gravity theory whose Lagrangian is given by a transgression form invariant under the Poincaré group.     

Topological susceptibility in SU(3) gauge theory

We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r(4)(0)chi = 0.059(3), which corresponds to chi = (191 +/- 5 MeV)(4) if F(K) is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the eta(').     

Tumbling and complementarity in a chiral gauge theory

We consider in detail a chiral SU(N) gauge theory which undergoes multiple tumbling. An extension of the notion of complementarity is used which allows us to deduce the set of massles fermions, in the confining phase of the theory, which we needed for anomaly matching. The likelihood of this confining phase ever being realized in practice is discussed.     

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.     

Proof of chiral symmetry breaking in lattice gauge theory

Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.     

Coulomb bare interactions in inhomogeneous 4-layer graphene structures

We investigate Coulomb bare interactions in 4-layer graphene systems, taking into account the inhomogeneity of dielectric environment. By solving Poisson equation in momentum space, 16 elements of Coulomb potential tensor have been formed with analytical expressions. The formulae illustrate that Coulomb bare interactions in inhomogeneous 4-layer graphene system differ noticeably from those in homogeneous one. Nevertheless, both intra- and interlayer Coulomb potentials become independent with dielectric constants of contacting media, but they are decided by those of dielectric layer surrounding the system in long wavelength approximation. Besides, numerical results demonstrate that Coulomb bare interactions decrease considerably with the increase in carrier density in graphene sheets as well as their separated distance. In all investigations, the inhomogeneity of dielectric background should not be neglected for improvement in the model.