Investigating Graphene-Based Systems: Interaction Effects, Localization, and Finite-Temperature Dynamics

Abstract

This dissertation presents a comprehensive theoretical and numerical investigation into the electronic properties of graphene‐based systems, with a focus on interaction effects, localization phenomena, and finite‐temperature dynamics. Motivated by graphene's exceptional electronic characteristics and its potential relevance for quantum technologies, the work systematically explores various graphene geometries—including two‐dimensional sheets, one‐dimensional nanoribbons, and hybrid junction ribbons. <br /> Central to the analysis is the application of the Hubbard model and tight-binding approximations to capture the essential physics of electron–electron interactions in low-dimensional carbon structures. The study delves into the topological and symmetry aspects of carbon nanoribbons, revealing how edge configurations and variations in ribbon width critically influence the material's electronic behavior. Advanced numerical techniques, such as Hamiltonian Monte Carlo, are employed to examine the localization of electronic states in the nonperturbative regime, offering quantitative insights into the energy distributions and wavefunction profiles of localized edge states. <br /> Furthermore, the dissertation develops an effective one-dimensional tight-binding framework for graphene nanoribbons with junctions, enabling a precise determination of low-energy constants and an assessment of interaction effects under finite-temperature conditions. The work also leverages thermal field theory to investigate the impact of thermal fluctuations on Hubbard interactions on a hexagonal lattice. <br /> Overall, the findings deepen our understanding of quantum phenomena in graphene-based materials and suggest several avenues for future research.