Interplay between geometry and topology on a conical quantum dot - Veiga, Leonardo Gomides (2020)
This work is aimed to the study of the interplay between quantum conﬁnement and topo- logical features in condensed matter systems with complex geometry. More speciﬁcally we studied a conical topological insulator quantum dot (CTIQD), where the local non- triviality of the cone tip (the cone has null curvature everywhere but at the tip, where there is a singularity) can lead to global eﬀects in the surface charge carriers and its energies spectrum and properties. We start by introducing an ordinary conical quantum dot (i.e., a semiconductor) through an eﬀective model , and we make an introduction to topology in condensed matter and topological insulators. The eﬀective Dirac operator that acts on the charge carriers on the surface of the conical topological insulator is calcu- lated, and the Dirac equation that describes the dynamics of these carriers is completely solved. We discussed the geometric and topological eﬀects associated with the singularity and how the wave function and the energy spectrum are aﬀected by these eﬀects. Keywords: Quantum dots. Topological insulators. Quantum conﬁnement. Dirac equation on curved spaces.