Tight binding Hamiltonian and energy dispersion relations in monolayer graphene

TANSO ◽  
2019 ◽  
Vol 2019 (289) ◽  
pp. 159-171
Author(s):  
Yoshihiro Hishiyama ◽  
Yutaka Kaburagi
Keyword(s):  
Tight Binding ◽  
Dispersion Relations ◽  
Monolayer Graphene ◽  
Energy Dispersion

scholarly journals GRAPHENE IN THE QUANTUM HALL REGIME: EFFECTS OF VACANCIES, SUBLATTICE POLARIZATION AND DISORDER

2009 ◽  
Vol 23 (12n13) ◽  
pp. 2618-2627 ◽  
Author(s):  
ANA L. C. PEREIRA ◽  
PETER A. SCHULZ
Keyword(s):  
Quantum Hall ◽  
Tight Binding ◽  
Wave Functions ◽  
Hall Resistance ◽  
Monolayer Graphene ◽  
Binding Model ◽  
Quantum Hall Regime ◽  
Hall Regime ◽  
Valley Polarization ◽  
Disorder Effect

We investigate the effects of vacancies, disorder and sublattice polarization on the electronic properties of a monolayer graphene in the quantum Hall regime. Energy spectra as a function of magnetic field and the localization properties of the states within the graphene Landau levels (LLs) are calculated through a tight-binding model. We first discuss our results considering vacancies in the lattice, where we show that vacancies introduce extra levels (or well-defined bands) between consecutive LLs. An striking consequence here is that extra Hall resistance plateaus are expected to emerge when an organized vacancy superlattice is considered. Secondly, we discuss the anomalous localization properties we have found for the lowest LL, where an increasing disorder is shown to enhance the wave functions delocalization (instead of inducing localization). This unexpected effect is shown to be directly related to the way disorder increasingly destroys the sublattice (valley) polarization of the states in the lowest LL. The reason why this anomalous disorder effect occurs only for the zero-energy LL is that, in absence of disorder, only for this level all the states are sublattice polarized, i.e., their wave functions have amplitudes in only one of the sublattices.

Exact energy-dispersion relations forN-well superlattice configurations

1990 ◽  
Vol 42 (15) ◽  
pp. 9552-9561 ◽  
Author(s):  
Richard L. Liboff ◽  
Steven R. Seidman
Keyword(s):  
Dispersion Relations ◽  
Energy Dispersion ◽  
Exact Energy

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.

scholarly journals Tight-binding dispersion of the prismatic pentagonal lattice

2018 ◽  
Vol 32 (01) ◽  
pp. 1750273
Author(s):  
Susobhan Paul ◽  
Asim Kumar Ghosh
Keyword(s):  
Band Structure ◽  
Density Of States ◽  
Parameter Space ◽  
Tight Binding ◽  
Dispersion Relations ◽  
Total Density ◽  
Zero Energy ◽  
Dirac Cone ◽  
Analytic Expressions ◽  
Total Density Of States

Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal lattice. Instead, a pair of van Hove singularities has been identified at two different energy values in the band structure.

Relativistic energy-dispersion relations of 2D rectangular lattices

2017 ◽  
Vol 31 (09) ◽  
pp. 1750061
Author(s):  
Engin Ata ◽  
Doğan Demirhan ◽  
Fevzi Büyükkılıç
Keyword(s):  
Dispersion Relations ◽  
Rectangular Lattice ◽  
Relativistic Energy ◽  
Spin States ◽  
Transfer Matrices ◽  
Energy Dispersion ◽  
Valence States ◽  
Relativistic Approach ◽  
Exactly Solvable ◽  
Rectangular Lattices

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters [Formula: see text], core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

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