Graphene Models In Relativistıc Quantum Mechanics

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2015

Student: KUBİLAY DURMUŞ

Supervisor: ÖZLEM YEŞİLTAŞ

Abstract:

Graphene which is a single atom layer thick sheets of carbon alined in a hexagonal or honeycomb lattice has become a very popular and important material in modern physics. By studying the fundamental quantum mechanical properties of this important material, perturbative additions in the Hamiltonian and their impacts on the dispersion relations and the spectrum under parity-time symmetry are discussed in this thesis. On the other hand, under various types of magnetic fields, such as constant and hyperbolic, the Dirac-Weyl equation is solved using the factorization method used in supersymmetric quantum mechanics for graphene fermions and the spectrum, probability and current densities are obtained. Further, factorization method and the polynomial methods are compared through the spinor compenents calculations.