Tight binding modeling of two dimensional and quasi-two dimensional materials
Author(s)
Advisor
Oğuz, GülserenDate
2017-09Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Since the advent of graphene, two-dimensional (2D) materials have consistently
been studied owing to their exceptional electronic and optical properties. While
graphene is completely two-dimensional in nature, its other analogues from the
group IV A elements in the periodic table have been proven to have a low-buckled
structure which adds up the exotic properties exhibited by them. The semiconductor
industry is striving for such materials exhibiting exotic electronic, optical
and mechanical properties.
In this thesis work we are primarily working towards a generalized tightbinding
(TB) model for the 2D family of group IV A elements. Graphene has
been studied extensively and we have successfully reproduced its energy bandstructure
accounting up to the third nearest neighbor contributions. The results
have been checked extensively by performing simulations over a large set of available
parameters and are found to be accurate. The other graphene analogues (viz;
silicene, germanene and stanene) exhibiting a hexagonal 2D structure have been
reported to have a buckling associated to them. We have analytically built up
a TB model by considering the orbital projections along the bond length which
accounts for the buckling in these 2D structures. Electronic band-structures have
been reproduced and compared by taking into account the nearest neighbor and
next-nearest neighbor contributions. Since these structures exhibit a Dirac like
cone at the Dirac point and showing linear dispersion, study of electronic bandstructures
in detail becomes indispensable.
After the famous Kane and Mele paper on Quantum Spin Hall E ect in
Graphene, condensed matter physicists have been looking for similar phenomena
in other 2D materials. We have successfully included the spin-orbit coupling (SOC) contribution to our unperturbed Hamiltonian and were able to produce
splitting around the Dirac points. Since, Silicene and its other analogues exhibit
same structure with di erent amount of buckling, we were able to track down the
whole energy band-structure. Alongside this thesis also focuses on calculating
optical properties of these materials.
In essence, this thesis work is an insight to the electronic and optical properties
of the hexagonal 2D structures from the carbon family group. Derived structures
from these 2D materials (viz; quantum dot, nano ribbon) could easily be studied
utilizing the tight-binding formulation presented here. The proposed future work
is the inclusion of nitrides and transition metal dichalcogenides (TMDCs) in the
TB model.
Keywords
TB ModelGraphene
Spin-orbit coupling
Buckling
Electronic Band- Structure
Optical properties