Green’s Functions for Tight Binding Hamiltonians

1979 ◽  
pp. 71-91 ◽  
Author(s):  
Eleftherios N. Economou
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding

scholarly journals Thermal bridging of graphene nanosheets via covalent molecular junctions: A non-equilibrium Green’s functions–density functional tight-binding study

Nano Research ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 791-799 ◽  
Author(s):  
Diego Martinez Gutierrez ◽  
Alessandro Di Pierro ◽  
Alessandro Pecchia ◽  
Leonardo Medrano Sandonas ◽  
Rafael Gutierrez ◽  
...  
Keyword(s):  
Density Functional ◽  
Green's Functions ◽  
Green’S Functions ◽  
Graphene Nanosheets ◽  
Tight Binding ◽  
Molecular Junctions ◽  
Binding Study ◽  
Thermal Bridging ◽  
Non Equilibrium

Computation of impurity Green’s functions in the tight-binding scheme

1983 ◽  
Vol 2 (3) ◽  
pp. 721-730 ◽  
Author(s):  
F. del Giallo ◽  
P. Moretti ◽  
F. Pieralli
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding

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.

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.

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.

Green's Functions for Tight-Binding Electrons on a Square Lattice in a Magnetic Field

1992 ◽  
Vol 170 (1) ◽  
pp. 163-170 ◽  
Author(s):  
R. Thamm ◽  
E. Kolley ◽  
W. Kolley
Keyword(s):  
Magnetic Field ◽  
Green's Functions ◽  
Green’S Functions ◽  
Tight Binding ◽  
Square Lattice

scholarly journals KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

2020 ◽  
Vol 7 (2) ◽  
pp. 191809 ◽  
Author(s):  
Simão M. João ◽  
Miša Anđelković ◽  
Lucian Covaci ◽  
Tatiana G. Rappoport ◽  
João M. V. P. Lopes ◽  
...  
Keyword(s):  
Electronic Structure ◽  
High Performance ◽  
Large Scale ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Density ◽  
Tight Binding ◽  
Spectral Expansion ◽  
Real Space ◽  
Disordered Crystals

We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals ( N ∼ 10 10 ). KITE’s core is written in C++, with a versatile Python-based interface, and is fully optimized for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green’s functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution. Several functionalities are demonstrated, ranging from simulations of local density of states and photo-emission spectroscopy of disordered materials to large-scale computations of optical conductivity tensors and real-space wave-packet propagation in the presence of magneto-static fields and spin–orbit coupling. On-the-fly calculations of real-space Green’s functions are carried out with an efficient domain decomposition technique, allowing KITE to achieve nearly ideal linear scaling in its multi-threading performance. Crystalline defects and disorder, including vacancies, adsorbates and charged impurity centres, can be easily set up with KITE’s intuitive interface, paving the way to user-friendly large-scale quantum simulations of equilibrium and non-equilibrium properties of molecules, disordered crystals and heterostructures subject to a variety of perturbations and external conditions.

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