Aspectos do acoplamento tipo excíton de Majorana unidimensionais

Abstract

This master’s thesis was dedicated to the study of a one-dimensional Majorana fermionic system in the position-dependent mass regime and subject to the energy conditions of a linear chain of particles. The purpose of this analysis is to investigate how the treatment of relativistic particles using common semiconductor approximations such, as effective mass theory and the tight-binding model affects the energy spectrum and thermodynamic properties of the system. To this end, central aspects of Relativistic Quantum Mechanics were reviewed, especially concepts related to the Dirac equation, the Majorana representation, and their applications in the context of solid state physics. Subsequently, the theory of effective mass in heterostructures was discussed, which was combined with the description of excitons to formulate a general equation for Majorana fermions with excitonic interactions. Finally, the presence of bound states was demonstrated and a canonical ensemble was constructed for the statistical analysis of the system.