scholarly journals Elastic Deformations and Wigner–Weyl Formalism in Graphene

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 317 ◽  
Author(s):  
I.V. Fialkovsky ◽  
M.A. Zubkov
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Solid State Physics ◽  
Binding Model ◽  
Elastic Deformations ◽  
Binding Models ◽  
External Electromagnetic Fields

We discuss the tight-binding models of solid state physics with the Z 2 sublattice symmetry in the presence of elastic deformations in an important particular case—the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles, the Wigner–Weyl formalism is explored. It allows the calculation of the two-point Green’s function in the presence of two slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters that result from elastic deformations. The developed formalism allows us to consider the influence of elastic deformations and the variations of magnetic field on the quantum Hall effect.

scholarly journals QUANTUM FIELD THEORY IN GRAPHENE

2012 ◽  
Vol 27 (15) ◽  
pp. 1260007 ◽  
Author(s):  
I. V. FIALKOVSKY ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Hall Effect ◽  
Faraday Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Polarization Operator ◽  
Quantum Field ◽  
Tight Binding Model ◽  
Binding Model

This is a short nontechnical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

scholarly journals QUANTUM FIELD THEORY IN GRAPHENE

2012 ◽  
Vol 14 ◽  
pp. 88-99 ◽  
Author(s):  
I. V. FIALKOVSKY ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Hall Effect ◽  
Faraday Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Polarization Operator ◽  
Quantum Field ◽  
Tight Binding Model ◽  
Binding Model

This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

TIGHT-BINDING MODEL FOR THE QUANTUM LADDER IN A MAGNETIC FIELD

1996 ◽  
Vol 10 (28) ◽  
pp. 3827-3856 ◽  
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Tight Binding ◽  
Critical Value ◽  
Tight Binding Model ◽  
Binding Model ◽  
First Case

A tight-binding model is formulated for the calculation of the electronic structure and the ground state energy of the quantum ladder under a magnetic field, where the magnetic flux at the nth plaquette is given by ϕn. First, the theory is applied to obtain the electronic spectra of the quantum ladder models with particular magnetic fluxes such as uniform magnetic fluxes, ϕn=0 and 1/2, and the staggered magnetic flux, ϕn= (−1)n+1ϕ0. From these, it is found that as the effect of electron hopping between two chains—the anisotropy parameter r=ty/tx—is increased, there are a metal-semimetal transition at r=0 and a semimetal–semiconductor transition at r=2 in the first case, and metal-semiconductor transitions at r=0 in the second and third cases. These transitions are thought of as a new category of metal-insulator transition due to the hopping anisotropy of the system. Second, using the spectrum, the ground state energy is calculated in terms of the parameter r. It is found that the ground state energy in the first case diverges as r becomes arbitrarily large, while that in the second and third cases can have the single or double well structure with respect to r, where the system is stable at some critical value of r=rc and the transition between the single and double well structures is associated with whether tx is less than a critical value of txc. The latter cases are very reminiscent of physics in polyacetylene studied by Su, Schrieffer and Heeger.

scholarly journals The electron density function of the Hückel (tight-binding) model

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170721 ◽  
Author(s):  
Ernesto Estrada
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Tight Binding ◽  
High Dimensional ◽  
Spin Interaction ◽  
Tight Binding Model ◽  
Solid State Physics ◽  
Binding Model ◽  
Conjugated Molecules ◽  
Unpaired Electrons

The Hückel (tight-binding) molecular orbital (HMO) method has found many applications in the chemistry of alternant conjugated molecules, such as polycyclic aromatic hydrocarbons (PAHs), fullerenes and graphene-like molecules, as well as in solid-state physics. In this paper, we found analytical expressions for the electron density matrix of the HMO method in terms of odd-powers of its Hamiltonian. We prove that the HMO density matrix induces an embedding of a molecule into a high-dimensional Euclidean space in which the separation between the atoms scales very well with the bond lengths of PAHs. We extend our approach to describe a quasi-correlated tight-binding model, which quantifies the number of unpaired electrons and the distribution of effectively unpaired electrons. In this case, we found that the corresponding density matrices induce embedding of the molecules into high-dimensional Euclidean spheres where the separation between the atoms contains information about the spin–spin repulsion between them. Using our approach, we found an analytic expression which explains the bond length alternation in polyenes inside the HMO framework. We also found that spin–spin interaction explains the alternation of distances between pairs of atoms separated by two bonds in conjugated molecules.

scholarly journals PT-symmetric graphene under a magnetic field

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160365 ◽  
Author(s):  
Fabio Bagarello ◽  
Naomichi Hatano
Keyword(s):  
Magnetic Field ◽  
Deformation Parameter ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Zero Energy ◽  
Binding Model ◽  
Energy States ◽  
The Asymmetry

We propose a P T -symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K ′ points, both in the P T -symmetric and P T -broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the P T -symmetric and P T -broken regions.

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