Narrow Results

We investigate in detail the transference of quantum states in a disordered channel. We consider a one-dimensional tight-binding model consisting of a source S connected to a receiver R throughout a disordered channel. The disorder distribution contains a single tunable spatial correlation length. We demonstrate that the disorder correlation length plays a relevant role within the localization properties of the channel. The hopping parameter between the sites S and R and the channel are also adjustable parameters. We investigate the possibility of transference of quantum states along this quantum channel model and describe the optimal conditions for the occurrence of a high fidelity process.

The exciton effects in 1-nm-wide armchair graphene nanoribbons (AGNRs) under the uniaxial strain were studied within the nonorthogonal tight-binding (TB) model, supplemented by the long-range Coulomb interactions. The obtained results show that both the excitation energy and exciton binding energy are modulated by the uniaxial strain. The variation of these energies depends on the ribbon family. In addition, the results show that the variation of the exciton binding energy is much weaker than the variation of excitation energy. Our results provide new guidance for the design of optomechanical systems based on graphene nanoribbons.

In this work, the influence of boron atom impurity is investigated on the electronic properties of a single-wall carbon nanotube superlattice which is connected by pentagon–heptagon topological defects along the circumference of the heterojunction of these superlattices. Our calculation is based on tight-binding $\pi$-electron method in nearest-neighbor approximation. The density of states (DOS) and electronic band structure in presence of boron impurity has been calculated. Results show that when boron atom impurity and nanotube atomic layers have increased, electronic band structure and the DOS have significant changes around the Fermi level.

We consider the semiclassical model of an extended tight-binding Hamiltonian comprising nearest- and next-to-nearest-neighbor interactions for a charged particle hopping in a lattice in the presence of a static arbitrary field and a rapidly oscillating uniform field. The application of Kapitza’s method yields a time-independent effective Hamiltonian with long-range hopping elements that depend on the external static and oscillating fields. Our calculations show that the semiclassical approximation is quite reliable as it yields, for a homogeneous oscillating field, the same effective hopping elements as those derived within the quantum approach. Besides, by controlling the oscillating field, we can engineer the interactions so as to suppress the otherwise dominant interactions (nearest neighbors) and leave as observable effects those due to the otherwise remanent interactions (distant neighbors).

Tight-binding models represent one of the basic approaches for studying the topological states of a matter. In the given account, we consider a tight-binding model set by a matrix Hamiltonian over 2D Brillouin zone. The corresponding multiband energy spectrum gives rise to non-Abelian gauge construction formed by the non-Abelian Berry connection $A_{\mu }$. The main gauge invariant quantities in such cases are the eigenvalues of Wilson loops. The purpose followed is the search for any special (on top of general) properties of Wilson loops for 2D tight-binding models which impose certain restrictions on the structure of its eigenvalues. The non-Abelian Berry connection is shown to be pure gauge with point-like singularities. The corresponding curvature tensor $F_{\mu \nu }={\partial }_{\mu }{A}_{\nu }-{\partial }_{\nu }{A}_{\mu }+i[A_{\mu },A_{\nu }]$ vanishes throughout the Brillouin zone except the isolated points where $F_{\mu \nu }$ is singular. Combining such behavior of $F_{\mu \nu }$ with non-Abelian Stokes theorem allows to avoid the path-ordering procedure in calculating the Wilson loops. In this approach, we show that Wilson loops are endowed by the group structure isomorphic to the fundamental group of the Brillouin zone. The latter is the Abelian group $Z\times Z$ forcing the set of eigenvalues of Wilson loops to comprise of two fixed phases associated with the two primitive elements (generators) of $Z\times Z$.

We investigate the optical conductivity in the two-dimensional (2D) square and triangular tight-binding lattice-electron model with staggered magnetic flux (SMF). The SMF results in a two-sublattice system with two branches of energy bands in both cases, and even generates new flux-dependent optical properties. Results for the flux parameter dependence of the mean kinetic energy, the Drude weight and the optical conductivity are discussed in detail. A comparison between the two cases has been done.

The quantum dynamics of a driven single-band tight-binding model with infinite and Dirichlet boundary conditions is considered. The polynomial algebra for the above model but with periodic boundary conditions (quantum ring) is constructed. Based on analyzing the algebraic structures of Hamiltonian, the solution of the time-dependent Schrödinger equation is also obtained exactly.

This paper presents a new method of describing electronic spectrum, thermodynamic potential, and electrical conductivity of disordered crystals based on the Hamiltonian of multi-electron system and diagram method for Green’s functions finding. Electronic states of a system were described by multi-band tight-binding model. The Hamiltonian of a system is defined on the basis of the wave functions of electron in the atom nucleus field. Electrons scattering on the oscillations of the crystal lattice are taken into account. The proposed method includes long-range Coulomb interaction of electrons at different sites of the lattice. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. Cluster expansion is obtained for density of states, free energy, and electrical conductivity of disordered systems. We show that contribution of the electron scattering processes to clusters is decreasing along with increasing number of sites in the cluster, which depends on small parameter. The computation accuracy is determined by renormalization precision of the vertex parts of the mass operators of electron-electron and electron-phonon interactions. This accuracy also can be determined by small parameter of cluster expansion for Green’s functions of electrons and phonons.

The graphene-on-substrates breaks the sub-lattice symmetry leading to the opening of a small gap. The small band gaps can be enhanced by electron–phonon interactions by keeping strongly polarized superstrate on graphene. To describe the band gap opening in graphene, we propose a tight-binding model Hamiltonian taking into account of third-nearest-neighbor electron-hoppings. We introduce repulsive Coulomb interaction at two sub-lattices of graphene. Further, we consider phonon coupling to the electron densities centered at two sub-lattices in the presence of phonon vibration with a single frequency. For high frequency phonons, the present interaction represents the Holstein interaction. Applying Lang–Firsov canonical transformation in the high phonon-frequency limit, we calculate the modified Coulomb interaction and the effective hopping integral which are functions of electron–phonon coupling, phonon-frequency and nearest-neighbor electron-hopping integral. The electron Green’s functions are calculated by Zubarevs technique. The electron occupancies at two sub-lattices for up and down spins are calculated and computed self-consistently. Finally, we calculate the modulated substrate induced gap of graphene-on-substrate, which is computed numerically for $100\times 100$ grid points for electron momentum. We have studied the interplay of Coulomb interaction, electron–phonon interaction in high phonon-frequency limit. The maximum band gap achieved due to the interplay is nearly 67% more than the substrate induced gap. To achieve this condition, one requires low Coulomb energy for low frequency phonon, while one needs high Coulomb interaction and high electron–phonon interaction of a given lattice vibration frequency. For given electron–phonon interaction and phonon-frequency, the modified gap is enhanced throughout the temperature range with increase of Coulomb interaction.