Long-range permeation of wave function and superficial surface state due to strong quantum size effects in topological Bi/BiSb heterojunctions

TL;DR

This paper investigates the quantum size effects in Bi/BiSb heterojunctions, revealing wave function permeation and challenging previous notions of surface states, with implications for topological insulator properties.

Contribution

It introduces a detailed theoretical analysis of quantum size effects in topological heterojunctions, showing unexpected band alignment and wave function behavior.

Findings

Wave functions permeate through 80-nm-thick heterojunctions.

One major spectrum from Bi surface is not the true surface state.

Findings may overturn previous understanding of Bi's topological surface state.

Abstract

The quantum size effect has a significant impact on electrons, such that it can even change their topologically protected properties. An example of this phenomenon is the gap opening in the topologically protected gapless surface state in finite-thickness topological-insulator films. However, much is not known about the quantum size effect in topological heterojunctions. In this study, by calculating the single-particle spectrum of Bi/Bi$_{1-x}$Sb$_{x}$ based on the well-known Liu-Allen model, we found that the strong quantum size effect in topological heterojunctions yields an unexpected band alignment. The wave functions permeate each other through the attached materials, and this occurs even in 80-nm-thick heterojunctions. Furthermore, we theoretically found that one of the two major spectra obtained from the Bi surface does not represent the true surface state of Bi. This finding may overturn the previous understanding of the topological surface state of Bi.