Tight-Binding Approximation for a Bloch Electron in a Magnetic Field

1969 ◽  
pp. 337-343 ◽  
Author(s):  
A. Rabinovitch
Keyword(s):  
Magnetic Field ◽  
Tight Binding ◽  
Tight Binding Approximation ◽  
Bloch Electron

AHARONOV–BOHM EFFECT ON QUANTUM TRANSPORT IN SINGLE-WALLED CARBON NANOTUBE INTERFEROMETERS

2010 ◽  
Vol 24 (09) ◽  
pp. 849-857 ◽  
Author(s):  
MEI HAN ◽  
YONG ZHANG
Keyword(s):  
Magnetic Field ◽  
Gate Voltage ◽  
Axial Magnetic Field ◽  
Tight Binding ◽  
Tube Length ◽  
Quantum Conductance ◽  
Tight Binding Approximation ◽  
Single Walled Carbon ◽  
Conductance Oscillation ◽  
Walled Carbon Nanotubes

The quantum conductance of the electron interferometers composed of the armchair and metallic zigzag single-walled carbon nanotubes (SWNTs) in an axial magnetic field lower than 100 T has been studied by using the tight-binding approximation and Landauer–Buttiker formula. Quantum conductance oscillation as a function of gate voltage due to Fabry–Perot like electron interference was found. The analytical expressions of the rapid and slow conductance oscillation periods for the armchair SWNTs have been derived. It is shown that they depend on the magnetic field, gate voltage, and tube length. For the case of the metallic zigzag SWNTs, except rapid conductance oscillation, slow conductance oscillation was also found, which should not exist without the axial magnetic field.

Surface-state energies and wave functions in layered organic conductors

2020 ◽  
Vol 75 (11) ◽  
pp. 987-998
Author(s):  
Danica Krstovska ◽  
Aleksandar Skeparovski
Keyword(s):  
Magnetic Field ◽  
Surface State ◽  
Tight Binding ◽  
Surface States ◽  
Organic Conductors ◽  
Wave Functions ◽  
Energy Dispersion ◽  
Quantization Rule ◽  
Tight Binding Approximation ◽  
Dispersion Law

AbstractWe have calculated and analyzed the surface-state energies and wave functions in quasi-two dimensional (Q2D) organic conductors in a magnetic field parallel to the surface. Two different forms for the electron energy spectrum are used in order to obtain more information on the elementary properties of surface states in these conductors. In addition, two mathematical approaches are implemented that include the eigenvalue and eigenstate problem as well as the quantization rule. We find significant differences in calculations of the surface-state energies arising from the specific form of the energy dispersion law. This is correlated with the different conditions needed to calculate the surface-state energies, magnetic field resonant values and the surface wave functions. The calculations reveal that the value of the coordinate of the electron orbit must be different for each state in order to numerically calculate the surface energies for one energy dispersion law, but it has the same value for each state for the other energy dispersion law. This allows to determine more accurately the geometric characteristics of the electron skipping trajectories in Q2D organic conductors. The possible reasons for differences associated with implementation of two distinct energy spectra are discussed. By comparing and analyzing the results we find that, when the energy dispersion law obtained within the tight-binding approximation is used the results are more relevant and reflect the Q2D nature of the organic conductors. This might be very important for studying the unique properties of these conductors and their wider application in organic electronics.

The Electronic Spectrum of Graphene

2011 ◽  
Vol 6 (3) ◽  
pp. 71-82
Author(s):  
Arkadiy A. Kozhevnikov
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Electronic Spectrum ◽  
Periodic Potential ◽  
Energy Levels ◽  
Tight Binding ◽  
Two Dimensional ◽  
Tight Binding Approximation

Based on the tight binding approximation for the energy levels of the electron in periodic potential, the electronic spectrum is found of the two-dimensional allotrope of the carbon called graphene. The problem of finding the Landau energy levels of graphene in external magnetic field is solved

scholarly journals Relativistic tight-binding approximation method for materials immersed in the magnetic field

2013 ◽  
Vol 38 (4) ◽  
pp. 663-665
Author(s):  
Katsuhiko Higuchi ◽  
Dipendra Bahadur Hamal ◽  
Kei Yamamoto ◽  
Masahiko Higuchi
Keyword(s):  
Magnetic Field ◽  
Approximation Method ◽  
Tight Binding ◽  
Tight Binding Approximation ◽  
The Magnetic Field

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.

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