Dirac Theory and Topological Phases of Silicon Nanotube

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.

5 pages, 5 figures

References in corpus (7)

• Quantum Spin Hall Effect in Silicene
• Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit gap of graphene: First-principles calculations
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field
• Quantum Hall Effects in Silicene

Cited by in corpus (6)

• Topological Phase Transition without Gap Closing
• Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene
• Thermal transport in silicene nanotubes: Effects of length, grain boundary and strain
• Hexagonally Warped Dirac Cones and Topological Phase Transition in Silicene Superstructure
• Structural stability and electronic properties of SP3 type silicon nanotubes
• Quantum phase transitions of topological insulators without gap closing