Dirac Theory and Topological Phases of Silicon Nanotube

TL;DR

This paper explores how electric fields can induce topological phase transitions in silicon nanotubes, leading to helical zero-energy modes that could serve as quantum wires for spintronics.

Contribution

It demonstrates the emergence of helical zero modes in silicon nanotubes under electric fields using Dirac theory, revealing new topological phases and localized wave functions.

Findings

Electric field induces topological phase transition in silicon nanotubes.

Four helical zero-energy modes appear beyond a critical electric field.

Zero modes are localized in metallic regions, suitable for spin transport.

Abstract

Silicon nanotube is constructed by rolling up a silicene, i.e., a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. It is a semiconductor or an insulator owing to relatively large spin-orbit interactions induced by its buckled structure. The key observation is that this buckled structure allows us to control the band structure by applying electric field $E_z$. When $E_z$ is larger than a certain critical value $E_{\text{cr}}$, by analyzing the band structure and also on the basis of the effective Dirac theory, we demonstrate the emergence of four helical zero-energy modes propagating along nanotube. Accordingly, a silicon nanotube contains three regions, namely, a topological insulator, a band insulator and a metallic region separating these two types of insulators. The wave function of each zero mode is localized within the metallic region, which may be used as a quantum wire to transport spin currents in future spintronics. We present an analytic expression of the wave function for each helical zero mode. These results are applicable also to germanium nanotube.