Quasistationary states in a quantum dot formed at the edge of a topological insulator by magnetic barriers with finite transparency

Abstract

A model of quasistationary states is constructed for the one-dimensional edge states propagating along the edge of a two-dimensional topological insulator based on HgTe/CdTe quantum well in the presence of magnetic barriers with finite transparency. The lifetimes of these quasistationary states are found analytically and numerically via different approaches including the solution of the stationary Schrödinger equation with complex energy and the solution of the transmission problem for a double barrier structure. The results can serve as a guide for determining the parameters of magnetic barriers creating the quantum dots where the lifetimes for the broadened discrete levels are long enough for manipulation with their occupation numbers by external fields.