Visualization and quantum computation of Moiré superconductivity in bilayer graphene, carbon nanocones and nanostrips

摘要

The purpose of this project is to visualize and study the electronic properties of carbon nanostructures. The principal structures studied are AA and AB (Bernal) stacked graphene bilayers, an 80C nanocone with pentagonal defects at its apex, and a 16C nanoring. Graphene and other based nanostructures have attracted much attention due to their unique electronic properties. For example, bilayer graphene shows superconductivity at certain magic angles of rotation. Open source molecular modeling and visualization programs like SAMSON, Avogadro, and VMD are utilized to generate the structures above. Using bond information in order to find nearest neighbors, an adjacency matrix can be generated from which the energy eigenvalues are solvable and are used to visualize the dispersion relation, free energy, persistent current, Green's function, and entanglement entropy. The goal of this project is to study the effect of rotation on the electronic properties of bilayer graphene, particularly as it pertains to the magic angle where superconductivity occurs, as well as the electronic properties of the bilayer Moire patterns which emerge due to the superposition of the identical lattices at different angles. An important goal is to incorporate phonon interactions into the tight-binding model for carbon structures, and to utilize quantum based computing as a tool to find the ground state properties of these structures, particularly in the terminating case where boundary conditions have an effect.