The Tight-Binding Study of the Temperature Dependent Anti-Ferromagnetic Order in Graphene

2018 ◽  
Vol 24 (8) ◽  
pp. 5970-5974
Author(s):  
H. S Gouda ◽  
Sivabrata Sahu ◽  
G. C Rout
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding ◽  
Nearest Neighbors ◽  
Hole Doping ◽  
Tight Binding Model ◽  
Temperature Dependent ◽  
Electron Hole ◽  
Binding Model ◽  
Model Study

We propose a tight binding model study for graphene taking the electron hopping up to third-nearest-neighbors. The graphene placed on different polarized substrates introduces in-equivalences in the two sub-lattices of honeycomb unit cell of graphene. Further the electron/hole doping in graphene enhances the in-equivalence in both the sub-lattices. The Hubbard type Coulomb interaction between the electrons in both sub-lattices generates anti-ferromagnetic (AFM) order in graphene under certain conditions. Zubarev’s Green’s functions method is applied to solve the Hamiltonian. The spins of the electron in the two sub-lattices are assumed to be oriented in opposite directions giving rise to AFM order in the system. The magnetization is calculated from the Green’s functions and computed self-consistently. The effect of the presence of substrates and doping concentrations on magnetization is reported here.

Tight-Binding Model Study of Tunneling Spectra of Monolayer Graphene-on-Substrate

2018 ◽  
Vol 17 (04) ◽  
pp. 1760027 ◽  
Author(s):  
Himanshu Sekhar Gouda ◽  
Sivabrata Sahu ◽  
G. C. Rout
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding ◽  
Mean Field Approximation ◽  
Coulomb Energy ◽  
Electron Interaction ◽  
Model Parameters ◽  
Tight Binding Model ◽  
Binding Model ◽  
Model Study

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 [Formula: see text] and [Formula: see text] 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 [Formula: see text] at [Formula: see text] sublattice and [Formula: see text] at [Formula: see text] site with [Formula: see text] and [Formula: see text] being the antiferromagnetic magnetizations at [Formula: see text] and [Formula: see text] 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.

Tight-binding model in the theory of disordered crystals

2020 ◽  
Vol 34 (19n20) ◽  
pp. 2040065
Author(s):  
S. Repetsky ◽  
I. Vyshyvana ◽  
S. Kruchinin ◽  
S. Bellucci
Keyword(s):  
Electrical Conductivity ◽  
Small Parameter ◽  
Cluster Expansion ◽  
Thermodynamic Potential ◽  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Binding Model ◽  
Diagram Method

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.

Model Study of the Role of Impurity on the Ferromagnetic Order in Graphene-on-Substrate

2018 ◽  
Vol 24 (8) ◽  
pp. 5960-5963
Author(s):  
Rashmirekha Swain ◽  
Sivabrata Sahu ◽  
G. C Rout
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding ◽  
Function Technique ◽  
Coulomb Energy ◽  
Ferromagnetic Order ◽  
Model Study ◽  
Strong Coulomb ◽  
Grid Points ◽  
Effect Of Doping

We report here a tight-binding calculation to investigate the effect of doping on the ferromagnetism in graphene supported by different substrates. The Hamiltonian consists of electron hoppings in the graphene upto third-nearest-neighbors. The substrate introduces in-equivalence in the two sub-lattices of carbon in the honey-comb lattice. The strong Coulomb correlation between electrons at the sub-lattices produces ferromagnetic order in the system. The doping introduces further in-equivalence in the sub-lattices and is expected to stabilize the ferromagnetic order. The Green’s functions are calculated by using Zubarev’s Green’s function technique. Finally the ferromagnetic magnetizations and hence the ferromagnetic gap are calculated from the electron correlations obtained from the corresponding electron Green’s functions. The ferromagnetic gap equation is computed numerically and self-consistently by using 100 × 100 grid points of the electron momentum. The effect of doping on the temperature dependent ferromagnetic gap is investigated by varying different doping concentrations, impurity potential and Coulomb energy.

scholarly journals TRANSPORT IN A CLEAN GRAPHENE SHEET AT FINITE TEMPERATURE AND FREQUENCY

2008 ◽  
Vol 22 (16) ◽  
pp. 2529-2536 ◽  
Author(s):  
N. M. R. PERES ◽  
T. STAUBER
Keyword(s):  
Graphene Sheet ◽  
Finite Temperature ◽  
Tight Binding ◽  
Dc Conductivity ◽  
Finite Conductivity ◽  
Tight Binding Model ◽  
Zero Temperature ◽  
Electron Hole ◽  
Binding Model ◽  
Field Theoretical Model

We calculate the conductivity of a clean graphene sheet at finite temperatures starting from the tight-binding model. We obtain a finite value for the dc-conductivity at zero temperature. For finite temperature, the spontaneous electron-hole creation, responsible for the finite conductivity at zero temperature, is washed out and the dc-conductivity yields zero. Our results are in agreement with calculations based on the field-theoretical model for graphene.

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