Extended Coupled Cluster approach to Twisted Graphene Layers

Abstract

Correlated systems are usually studied using the normal coupled cluster method. Unfortunately, this method is only a small subset of the actual description of such systems, with symmetry-breaking, required for studying phase transitions, not permitted. Additionally, in the strong correlation regime it is known to breakdown. Therefore, in this dissertation a workflow for the extended coupled cluster framework is presented up to doubles truncation. This is done using the particle-hole formalism in order to produce manageable algebra with automatic differentiation as a way to solve the equations. It is further discussed to be equivalent to adding correlation treatment directly to Hartree-Fock. A novel study of correlation effects in twisted bilayer graphene is presented as a practical application. This is accomplished by using the Bistritzer-MacDonald model with a double metallic gate potential to account for electrostatic interactions in an experimental setting. Simulations at singles truncation agreed with previous Hartree-Fock studies, while correlation effects at doubles truncation showed insignificant contributions to the band structure, but a relatively significant increase of the Fermi level, indicating lower filling requirements for the phase transition. Tensor contraction is suggested as a way to significantly reduce the computational cost of this workflow and permit studies of valley and spin effects as well as other larger systems.

Date of Award	31 Dec 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Niels Walet (Supervisor) & Yang Xian (Supervisor)