Tight binding investigation of graphene nanostructures under magnetic field

Yalçın, Fırat
Electrons moving under the effects of a two dimensional periodic potential and a magnetic field perpendicular to this two dimensional plane has been the focus of many different studies for a long time. The interplay between the two length scales in this problem, lattice constant and the characteristic magnetic length, results in interesting phenomena such as the Hofstadter's butterfly. The bulk of the studies done so far has focused on uniform magnetic fields. The only requirement for the vector potential is that its closed loop integral resulting in the correct flux piercing through the loop. This allows us to use a rather unconventional gauge where we set certain values for the line integrals instead of solving the line integrals with a known vector potential. Using this gauge, we can study the effects of inhomogeneous fields in a very efficient way. The electronic structures of hexagonal flakes, Y-shaped junctions and cross-shaped junctions of different sizes have been studied using tight-binding method and the optimal gauge. The results show emergence of new states around the Fermi level localized on the lattice sites where the magnetic fields are applied.


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Gurcan, OD; Mirnov, VV; Ucer, D (2000-05-01)
Radial motion of a highly conducting sphere in external magnetic field is considered. It both perturbs the external magnetic field and generates an electric field. Exact analytic solution has been obtained previously for a uniformly expanding sphere. In the present paper a new exact solution is derived which is valid not only for expansion but for contraction as well. It allows us to calculate analytically the total electromagnetic energy irradiated by the sphere involved in periodical radial motion with ar...
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We study the nonlinear intersubband optical absorption of a single Si delta-doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schrodinger and Poisson equations are solved self-consistently for various electric field strengths. The self-consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed wit...
ILAIWI, KF; Tomak, Mehmet (Wiley, 1991-08-01)
The polarization of a quantum electron confined in square, parabolic, and triangular quantum wells is calculated numerically. The aim of the present calculations is to compare the results for various geometries.
Nonlinear optical properties of a Woods-Saxon quantum dot under an electric field
AYTEKİN, ÖZLEM; Turgut, Sadi; Unal, V. Ustoglu; Aksahin, E.; Tomak, Mehmet (Elsevier BV, 2013-12-01)
A theoretical study of the effect of the confining potential on the nonlinear optical properties of two dimensional quantum dots is performed. A three-parameter Woods-Saxon potential is used within the density matrix formalism. The control of confinement by three parameters and an applied electric field gives one quite an advantage in studying their effects on the nonlinear properties. The coefficients investigated include the optical rectification, second and third-harmonic generation and the change in the...
Electronic properties of a large quantum dot at a finite temperature
Gulveren, B; Atav, U; Tomak, Mehmet (Elsevier BV, 2005-09-01)
The physical properties of a two-dimensional parabolic quantum dot composed of large number of interacting electrons are numerically determined by the Thomas Fermi (TF) method at a finite temperature. Analytical solutions are given for zero temperature for comparative purposes. The exact solution of the TF equation is obtained for the non-interacting system at finite temperatures. The effect of the number of particles and temperature on the properties are investigated both for interacting and non-interactin...
Citation Formats
F. Yalçın, “Tight binding investigation of graphene nanostructures under magnetic field,” M.S. - Master of Science, Middle East Technical University, 2019.