Exploring the Fractional Quantum Hall Effect and Electron-Electron Interactions in ABA Trilayer Graphene through Electric Fields

Abstract

Since the discovery of graphene (a single sheet of carbon atoms) in 2004, the field has expanded with groundbreaking discoveries like the Quantum Hall effect, correlated phenomena, superconductivity, and ferromagnetism. Adding more layers to graphene allows one to access additional degree of freedom. With an increase in the number of layers, bands become flatter. This provides an ideal setting for observing unconventional superconductivity and various correlated phenomena, which have been recently observed in ABC trilayer graphene and Bernal stacked bilayer graphene. Such multilayer graphene systems also provide a platform where the band structure can be engineered with an external displacement field. This tunability has led to observing various electron-electron correlated phenomena such as fractional quantum Hall effect, quantum Hall ferromagnetism phases, and spontaneous breaking of C3 rotational symmetry. In this thesis, we focus on the ABA stacked trilayer graphene. It is a multiband system. At zero interlayer potential, it is composed of a monolayer-like and a bilayer-like band. This allows the study of the massless and massive electron behavior simultaneously in a single system. The bands can be tuned by applying external interlayer potential, providing further control over the electronic properties. In this thesis, we focus on the system’s integer and fractional quantum Hall states and the effect of interlayer potential on these states.