Interesting features of the edge states in topological quantum dots.

Quantum dots made of topological insulators, known as topological quantum dots, have attracted much interest in recent years. We investigate theoretically the electronic properties of topological quantum dots formed by etching two dimensional topological insulators, using the method of mode-matching, which gives more rigorous results than the expansion approach used in previous studies. We find that the edge state energy of the quantum dot is affected by its radius R. For each fixed angular momentum index, there exists a critical R below which there would be no edge states. For quantum dots with large R , the energy spectrum of the edge states is almost equidistant, which is interesting and rare in low dimensional solid systems without external driving field. The nearly uniform energy spacing shows almost a linear dependence on 1∕ R and the corresponding optical transition frequency can be in the terahertz band. • Edge states of the topological quantum dot are affected by its radius. • Topological quantum dot with radius less than a critical value has no edge states. • The edge states energy levels are equidistant for quantum dot with large enough radius. • The transition frequency between the equally spaced energy levels can be in the terahertz band. [ABSTRACT FROM AUTHOR]