Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers

Abstract A model of bound state formation from the delocalized edge states of 2D topological insulator (TI) is derived by considering the effects of magnetic barriers attached to the edge of the HgTe/CdTe quantum well. The resulting structure has a spatial form of 1D quantum dot (QD) with variable number of bound states depending on barrier parameters. The spatial profile of exchange interaction between the edge states and barriers is derived from the interaction with single impurity magnetic moment and is generalized for the barrier bulk structure formed by ensemble of impurities. The resulting Hamiltonian is studied as a function of barrier parameters including their strength and orientation of the magnetic moments. It is shown that for parallel magnetization of two barriers at least two discrete levels are formed regardless of the barrier strength. For antiparallel magnetization at least a single bound state is formed for any strength of the barriers. Our results may help in design of novel types of QDs based on TIs.