Multifractal properties of the wave functions of the square-lattice tight-binding model with next-nearest-neighbor hopping in a magnetic field

1997 ◽  
Vol 55 (19) ◽  
pp. 12971-12975 ◽  
Author(s):  
I. Chang ◽  
K. Ikezawa ◽  
M. Kohmoto
Keyword(s):  
Magnetic Field ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Wave Functions ◽  
Square Lattice ◽  
Tight Binding Model ◽  
Binding Model

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 Accurate six-band nearest-neighbor tight-binding model for the π-bands of bulk graphene and graphene nanoribbons

2011 ◽  
Vol 109 (10) ◽  
pp. 104304 ◽  
Author(s):  
Timothy B. Boykin ◽  
Mathieu Luisier ◽  
Gerhard Klimeck ◽  
Xueping Jiang ◽  
Neerav Kharche ◽  
...  
Keyword(s):  
Nearest Neighbor ◽  
Graphene Nanoribbons ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Binding Model

scholarly journals ON THE VERDET CONSTANT AND FARADAY ROTATION FOR GRAPHENE-LIKE MATERIALS

2013 ◽  
Vol 25 (04) ◽  
pp. 1350007 ◽  
Author(s):  
MIKKEL H. BRYNILDSEN ◽  
HORIA D. CORNEAN
Keyword(s):  
Taylor Expansion ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Transverse Component ◽  
Tight Binding Model ◽  
Binding Model ◽  
Gauge Invariant ◽  
Verdet Constant ◽  
Absolute Value ◽  
Computable Formula

We present a rigorous and rather self-contained analysis of the Verdet constant in graphene-like materials. We apply the gauge-invariant magnetic perturbation theory to a nearest-neighbor tight-binding model and obtain a relatively simple and exactly computable formula for the Verdet constant, at all temperatures and all frequencies of sufficiently large absolute value. Moreover, for the standard nearest-neighbor tight-binding model of graphene we show that the transverse component of the conductivity tensor has an asymptotic Taylor expansion in the external magnetic field where all the coefficients of even powers are zero.

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 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.

Quantum cascade laser gain medium modeling using a second-nearest-neighbor tight-binding model

2005 ◽  
Vol 37 (6) ◽  
pp. 410-424 ◽  
Author(s):  
Jeremy Green ◽  
Timothy B. Boykin ◽  
Corrie D. Farmer ◽  
Michel Garcia ◽  
Charles N. Ironside ◽  
...  
Keyword(s):  
Quantum Cascade Laser ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Gain Medium ◽  
Tight Binding Model ◽  
Binding Model ◽  
Quantum Cascade ◽  
Laser Gain
Sign in / Sign up

Export Citation Format

Share Document