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The pristine graphene is a zero band gap semiconductor with valence and conduction bands touching each other at Dirac points. The graphene-on-substrate exhibits a small gap at the Dirac points. The microscopic Hamiltonian describes the nearest-neighbor -electron hopping with tight-binding approach. Graphene-on-substrate exhibits a gap at the Dirac points where the energy at A sublattice is raised by and the energy at B sublattice is lowered by energy leading to asymmetry in the two sublattices. Further, we have introduced impurities at both the sublattices. The Coulomb interaction in graphene-on-substrate is described by Hubbard-type Coulomb interaction with energy U. The Coulomb interaction is treated in the calculation within the mean-field approximation in the paramagnetic limit. The temperature-dependent site-independent electron occupancies at both the sublattices are calculated and computed self-consistently. The difference between the electron occupancies of both the sublattices introduces a charge gap. The effect of charge gap on the electronic band dispersion in graphene-on-substrate is investigated by varying different model parameters of the system like Coulomb energy, substrate-induced gap, temperature, total band filling and impurity concentrations. It is observed that both the valence and conduction bands are shifted above the Fermi level exhibiting a charge gap between the bands. As a result, the partially filled valence band exhibits metallic behavior. [ABSTRACT FROM AUTHOR]

The graphene-on-substrate in the presence of impurity exhibits ferromagnetism. In the present paper, we propose a tight-binding Hamiltonian model which consists of electron hopping upto-third-nearest-neighbors. The graphene-on-substrate develops a gap of few meV. This Hamiltonian incorporates a gap of energy at A sub-lattice and a gap of energy at B sub-lattice. The Hamiltonian describes the impurity effect at A and B sub-lattices with the impurity potential describing hole and/or electron doping. The on-site Coulomb interaction at A and B sub-lattices is described by Hubbard type repulsive Coulomb interaction which is considered within the mean-field approximation having ferromagnetic magnetization of two different magnitudes at the sub-lattices. The total Hamiltonian is solved by Zubarev's Green's function technique. The temperature-dependent ferromagnetic magnetizations are solved self-consistently taking grid points of the electron momentum. The electron band dispersion splits into four for A site and four for B site and the combined band dispersion exhibits eight bands for up/down spin orientations. The evolution of the band dispersion is investigated by varying different model parameters of graphene. [ABSTRACT FROM AUTHOR]

We report here the theoretical model study of antiferromagnetic ordering in graphene. We propose a tight-binding model Hamiltonian describing electron hopping up to third-nearest neighbors in graphene. The Hamiltonian describing inequivalence of and sublattices in graphene-on-substrate is incorporated. The Hubbard-type repulsive Coulomb interaction is considered for both the sublattices with same Coulomb energy. The electron-electron interaction is considered within mean-field approximation with mean electron occupancies at sublattice and at site with and being the antiferromagnetic magnetizations at and sublattices, respectively. The total Hamiltonian is solved by Zubarev's techniques of double time single particle Green's functions. The magnetizations are calculated from the correlation functions corresponding to the respective Green's functions. The temperature-dependent magnetizations are solved self-consistently taking suitable grid points for the electron momentum. Finally, the electron density of states (DOS) which is proportional to imaginary part of the electron Green's functions is calculated and computed numerically at a given temperature varying different model parameters for the system. The conductance spectra show a gap near the Dirac point due to substrate-induced gap and magnetic gap, while the van Hove singularities split into eight peaks due to two different sublattice magnetizations and two different spin orientations of the electron in graphene-on-substrate. [ABSTRACT FROM AUTHOR]

Doublet splitting of single-electron peaks has been observed in the conductance of a small high-resistance ring interferometer. Realistic modeling of the device shows that the electron system of interferometer divides into two triangular quantum dots connected by single-mode channels to each other and to reservoirs. We explain the splitting of conductance peaks by charge interaction of the dots. [ABSTRACT FROM AUTHOR]