We prove localization and probabilistic bounds on the minimum level spacing for Anderson tight-binding model lattice in any dimension, with single-site potential having a discrete distribution taking [Formula: see text] values, large. These results hold all energies under an assumption of weak hopping.

 The two-dimensional structure of graphene, consisting of an isotropic hexagonal lattice of carbon atoms, shows fascinating electronic properties, such as a gapless energy band and Dirac fermion behavior of electrons at fermi surface. Anisotropy can be induced in this structure by electrochemical pressure. In this article, by using tight-binding method, we review anisotropy effects in the elect...

Due to the high cost of experimental analyses, researchers used atomistic modeling methods for predicting the mechanical behavior of the materials in the fields of nanotechnology. In the pre-sent study the Self-Consistent Charge Density Functional Tight-Binding (SCC-DFTB) was used to calculate Young's moduli and average potential energy of the straight and curved graphenes with different curvat...

We report on an introductory study used to gauge the significance of random weakedge disorder on the coherent transport properties of ultra-thin zig-zag nanoribbons (ZGNRs) beyond the simple (i.e., first nearest-neighbour) tight-binding approximation. Such extensions include up to third nearest-neighbour hopping in an extended tight-binding model, as well as a mean-field Hubbard-U . The effect ...

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices ...

The energy spectrum and eigenstates of single-layer black phosphorous nanoribbons in the presence of perpendicular magnetic field and in-plane transverse electric field are investigated by means of a tight-binding method and the effect of different types of edges is analytically examined. A description based on a new continuous model is proposed by expansion of the tight-binding model in the lo...

We formalize the parity effect of a multichannel ring coupled to a side branch using the tight binding model. We find that the tight binding model gives slightly different result from the continuum model. We also show that some states of the system can be nonmagnetic. In the multichannel ring coupled to a side branch, the persistent current in the ring does not change sign, over gigantic fluctu...

We describe a simple graphene nanoribbon and bottom gate system and present numerical algorithms for solving Poisson’s and Thomas–Fermi equations for electrons in the graphene nanoribbon. The Poisson’s equation is solved using finite difference and finite element methods. Using the Poisson and Thomas–Fermi equations we calculate an electrostatic potential and surface electron density in the gra...