Topological phases in two-dimensional systems

Abstract

In this thesis, we investigate the emergence of topological properties in two-dimensional (2D) systems. We perform the calculations using density functional theory and tight-binding methods. The first system we investigate is a bismuth monolayer, a well-known topological insulator, doped with magnetic atoms. Our calculations show that the introduced magnetic perturbation does not affect the topological phase. Notably, we verify that when the impurities are located near the edge, a long-range coupling arises between them. Additionally, we note the occurrence of two magnetic phase transitions as a function of the inter-impurity distance, a signature of Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. These conclusions are validated by means of the derived RKKY Hamiltonian, whose results show good agreement with DFT calculations. The second topological phase investigate in this work emerges in graphenylene-like porous SiGe and Ge structures. We find fourfold degenerate band crossings which, under spin-orbit coupling, split into a pair of Weyl points. Their topological properties are confirmed through Weyl chirality and Berry curvature calculations. These conclusions are supported by the bulk-boundary correspondence, where we verify topological edge states (2D Fermi arcs) connecting Weyl points with opposite chiralities. Finally, we study the quantum anomalous Hall effect in extremely biaxial tensile strained 1T-CrX2 (X = Bi, Sb) monolayers. This topological phase arises from the interplay of spin-orbit coupling, many-body effects and biaxial tensile strain. Topological edge states are also observed, consistent with the bulk-boundary correspondence. The results of this investigation extend the list of two-dimensional magnetic materials, in which we predict the stability of the free standing 1T-CrBi2 monolayer. For both systems, our calculations show Curie temperatures above 160 K, which provides valuable findings for the quantum anomalous Hall context.