Bükülmüş iki katmanlı grafenin geometrisinin, enerjitik ve elektronik yapısının incelenmesi

Twisted bilayer graphene (TBG) manifests unique electronic properties that hold substantial potential for advancements in nanotechnology, material science, and quantum computing. In this thesis, critical insights into the fundamental charac- teristics of TBG are uncovered through an in-depth exploration of its geometric configurations, interlayer interactions, and electronic properties. We begin our investigation with a thorough analysis of the geometrical prop- erties of the twisted bilayer graphene. By plotting the unit cell size against twist angles, we uncover distinct patterns and symmetries that emerge at different an- gles, offering insights into the fundamental structural properties that influence the material's behavior. Following this, we examine the interlayer energies using both Lennard-Jones (LJ) and Kolmogorov-Crespi (KC) potentials. Our analysis of local stacking configurations reveals that the interlayer energy remains invariant due to the averaging contributions from AA and AB regions. We then analyze the band structures across various twist angles using tight- binding calculations, computing parameters such as Fermi velocity and effective mass of the electrons. We observe the emergence of flat bands at "magic angles" and other unique band structures at specific twist angles, highlighting the complex electronic behavior of TBG.