Quantum Coherence and W_infty*SU(2) Algebra in Bilayer Quantum Hall Systems

We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-Level projection taken into account. The symmetry group is found to be W_infty*SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excitations are topological solitons in this coherent mode. We point out that they are detectable by measuring the Hall current distribution.Comment: 15pages, Phys. Lett. A (in press

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

Improved Composite-Boson Theory of Monolayer and Bilayer Quantum Hall Ferromagnets

An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.Comment: 14 pages including 1 figure; Physics Letters A (to be published

SU(4) Coherent Effects to the Canted Antiferromagnetic Phase in Bilayer Quantum Hall Systems at ν\nu=2

In bilayer quantum Hall (BLQH) systems at $\nu$=2, three different kinds of ground states are expected to be realized, i.e. a spin polarized phase (spin phase), a pseudospin polarized phase (ppin phase) and a canted antiferromagnetic phase (C-phase). An SU(4) scheme gives a powerful tool to investigate BLQH systems which have not only the spin SU(2) but also the layer (pseudospin) SU(2) degrees of freedom. In this paper, we discuss an origin of the C-phase in the SU(4) context and investigate SU(4) coherent effects to it. We show peculiar operators in the SU(4) group which do not exist in SU$_{\text{spin}}$(2)$\otimes$SU$_{\text{ppin}}$(2) group play a key role to its realization. It is also pointed out that not only spins but also pseudospins are ``canted'' in the C-phase.Comment: 8 pages, 4 figures and 1 tabl

Anomalous Stability of nu=1 Bilayer Quantum Hall State

We have studied the fractional and integer quantum Hall (QH) effects in a high-mobility double-layer two-dimensional electron system. We have compared the "stability" of the QH state in balanced and unbalanced double quantum wells. The behavior of the n=1 QH state is found to be strikingly different from all others. It is anomalously stable, though all other states decay, as the electron density is made unbalanced between the two quantum wells. We interpret the peculiar features of the nu=1 state as the consequences of the interlayer quantum coherence developed spontaneously on the basis of the composite-boson picture.Comment: 5 pages, 6 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

Graphene Nanoribbon and Graphene Nanodisk

We study electronic properties of graphene derivatives which have closed edges. They are finite-length graphene nanoribbons and graphene nanodisks. No metallic states are found in finite-length zigzag nanoribbons though all infinite-length zigzag nanoribbons are metallic. We also study hexagonal, parallelogrammic and trigonal nanodisks with zigzag or armchair edges. No metallic states are found in these nanodisks either except trigonal zigzag nanodisks. It is interesting that we can design the degeneracy of the metallic states arbitrarily in trigonal zigzag nanodisks by changing the size.Comment: 7 pages, 5 figures, to be published in Physica E (EP2DS-17, Genova