Dirac Theory and Topological Phases of Silicon Nanotube

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.Comment: 5 pages, 5 figure

Single Dirac-Cone State and Quantum Hall Effects in Honeycomb Structure

A honeycomb lattice system has four types of Dirac electrons corresponding to the spin and valley degrees of freedom. We consider a state that contains only one type of massless electrons and three types of massive ones, which we call the single Dirac-cone state. We analyze quantum Hall (QH) effects in this state. We make a detailed investigation of the Chern and spin-Chern numbers. We make clear the origin of unconventional QH effects discovered in graphene. We also show that the single Dirac-cone state may have arbitrary large spin-Chern numbers in magnetic field. Such a state will be generated in antiferromagnetic transition-metal oxides under electric field or silicene with antiferromagnetic order under electric field.Comment: 5 pages, 5 figure

Spin Filter, Spin Amplifier and Other Spintronic Applications in Graphene Nanodisks

Graphene nanodisk is a graphene derivative with a closed edge. The trigonal zigzag nanodisk with size $N$ has $N$-fold degenerated zero-energy states. A nanodisk can be interpletted as a quantum dot with an internal degree of freedom. The grand state of nanodisk has been argued to be a quasi-ferromagnet, which is a ferromagnetic-like states with a finite but very long life time. We investigate the spin-filter effects in the system made of nanodisks and leads based on the master equation. The finite-size effect on spin filter is intriguing due to a reaction from the polarization of incoming current to a quasi-ferromagnet. Analyzing the relaxation process with the use of the Landau-Lifshitz-Gilbert equation, we explore the response to four types of incoming currents, namely, unpolarized current, perfectly polarized current, partially polarized current and pulse polarized current. We propose some applications for spintronics, such as spin memory, spin amplifier, spin valve, spin-field-effect transistor and spin diode.Comment: 10 pages, 10 figure