Extra Seminar - Würzburg ToCoTronics Colloquium

This talk explores the derivation and characterization of effective Hamiltonians for topological insulators using the downfolding technique. The primary objective is to demonstrate how this method can systematically separate the dynamics of low energy edge states from the bulk of the system. After establishing the theoretical formalism, we will examine the extraction of effective edge Hamiltonians through analytical approaches for the Su-Scrieffer-Heeger (SSH) and Qi-Wu-Zhang (QWZ) models. The core of the presentation will then focus on the numerical extension of the downfolding technique to the Bernevig-Hughes-Zhang (BHZ) model. Specifically, we will analyze the effects of Rashba spin-orbit coupling and bulk inversion asymmetry. The results provide a rigorous framework for understanding how such interactions modify the underlying system, highlighting the versatility of this method in the study of topological edge states.