summary.tex

\chapter{Summary}

As a result of this work open-source Python package for Tight Binding calculation appeared. 

I investigated diamond's energy band structure and showed that results agree with the results of TB calculations provided in the literature. However according to the calculated band structure diamond has direct band gap in $\Gamma$ point, whereas real diamond crystal is characterized by indirect band gap.

I studied graphene starting with the simplest model. Next I introduced expanded set of orbitals and nontrivial overlap matrix. And finally I showed, that intrinsic band gap due to spin orbit coupling appears in graphene when $d$ orbitals are taken into account.

At the last part of my work I investigated graphene nanoribbons and showed that band structure and their character depend on the nanoribbons' edges and their width. Also I studied density of states of the system with reduced periodicity. It appears, that size of sample crystal of the order of $100$ atoms is enough to describe crystal using wave-vector formalism.