Browsing by Subject "Tight-binding"

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Open Access
Investigation of geometry, energetics and electronic structure of twisted bilayer graphene
(2024-08) Amine, Nouha
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 properties of the twisted bilayer graphene. By plotting the unit cell size against twist angles, we uncover distinct patterns and symmetries that emerge at different angles, 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.
Open Access
P band in a rotating optical lattice
(The American Physical Society, 2008) Umucalılar, R. O.; Oktel, M. Ö.
We investigate the effects of rotation on the excited bands of a tight-binding lattice, focusing particularly on the first excited (p) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a nontrivial splitting and magnetic fine structure of the p band. We show that Peierls substitution can be modified to describe p band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first-principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p band can be investigated starting from this effective Hamiltonian.