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My thesis projects
Bachelor
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Quantum geometry in two-dimensional materials
Luis E. Sánchez
Autonomus University of Coahuila (UAdeC), Apr 2023
Two-dimensional materials have great potential to lead the next generation of electronic devices due to their unique physical properties. In particular, topological insulators are notable for their ability to conduct electricity on their edges, unlike conventional insulators which do not have this property. Furthermore, quantum geometry focuses on the study of the geometric properties of wave functions of quantum systems in Hilbert space. The most well-known properties are the Berry phase and curvature, which provide information on the topological phases and predict the existence of edge states. In this thesis, we study the topological properties of hexagonal crystalline structures, focusing on the descriptions of different systems obtaining exact analytical solutions and, occasionally, through numerical solutions. Specifically, we analyze pristine graphene, graphene with mass, and the Haldane model. We obtain analytical forms for the Berry curvature and phase, thus characterizing the different topological phases. Additionally, we explore the bulk-boundary correspondence, which relates the topological properties of the periodic system to the presence of edge states in the finite system
Thesis submitted for the Bachelor’s degree of Science in Engineering Physics.
Thesis supervisors: Pierre A. Pantaleón (IMDEA Nanoscience) and Carlos E. Rodríguez (UAdeC)
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Quantum transport in Kekulé-modulated in two-dimensional materials
Luis E. Sánchez
Autonomus University of Baja California (UABC), Aug 2025
Thesis submitted for the Master’s degree of Science in Physics.
Thesis supervisors: Ramón Carrillo-Bastos