Electron Tunneling in Single and Bilayer Graphene Heterojunctions

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Graphene, a crystalline two-dimensional monolayer of carbon atoms, is regarded as one of the most intriguing carbon allotropes. Owing to its distinct properties and the exceptional characteristics of its charge carriers, graphene has become a focal point for extensive theoretical and experimental research. Recent studies have revealed the experimental feasibility of creating graphene heterojunctions, which are formed by interconnecting flakes of bilayer graphene with single-layer graphene. In this thesis, we explore electron tunneling in single-bilayer heterojunctions employing a continuum model. Specifically, we investigate the influence of the terminated edge type, which can manifest as either zigzag or armchair edges, on the transport properties. Our analysis encompasses the computation of key quantities, including transmission and reflection probabilities, as well as conductance. Additionally, we introduce an electrostatic voltage as a means to provide external control over quantum transport within these heterojunctions. The results reveal the efficiency of the gate voltage controlling the quantum transport with armchair edges, while its impact on zigzag edges is notably limited. Finally, we show the effect of system geometry, particularly the width of the graphene flakes, to elucidate its role in electron tunneling characteristics. Our findings pave the way for valuable insights into quantum transport within graphene heterojunctions, offering guidance for experimental investigations and the optimization of system parameters to enhance their practical applications.