Well-localized edge states in two-dimensional topological insulators: ultrathin Bi films

We theoretically study the generic behavior of the penetration depth of the edge states in two-dimensional quantum spin Hall systems. We found that the momentum-space width of the edge-state dispersion scales with the inverse of the penetration depth. As an example of well-localized edge states, we take the Bi(111) ultrathin film. Its edge states are found to extend almost over the whole Brillouin zone. Correspondingly, the bismuth (111) 1-bilayer system is proposed to have well-localized edge states in contrast to the HgTe quantum well.Comment: 4 pages, 4 figure

Decoherence in Phase Space

Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.Comment: in press in Laser Phys.13(2003

Spin symmetry and spin current of helicity eigenstates of the Luttinger Hamiltonian

A general spin symmetry argument is proposed for spin currents in semiconductors. In particular, due to the symmetry with respect to spin polarization of the helicity eigenstates of the Luttinger Hamiltonian for a hole-doped semiconductor, the spin polarized flux from a single helicity eigenstate induced by an external electric field, is canceled exactly when all such contributions from eigenstates that are degenerate in energy are summed. Thus, the net spin current predicted by Murakami et al, Science 301, 1348 (2003), cannot be produced by such a Hamiltonian. Possible symmetry breaking mechanisms which may generate a spin current are discussed

Intrinsic spin Hall effect in platinum metal

Spin Hall effect in metallic Pt is studied with first-principles relativistic band calculations. It is found that intrinsic spin Hall conductivity (SHC) is as large as $\sim 2000 (\hbar/e)(\Omega {\rm cm})^{-1}$ at low temperature, and decreases down to $\sim 200 (\hbar/e)(\Omega {\rm cm})^{-1}$ at room temperature. It is due to the resonant contribution from the spin-orbit splitting of the doubly degenerated $d$-bands at high-symmetry $L$ and $X$ points near the Fermi level. By modeling these near degeneracies by effective Hamiltonian, we show that SHC has a peak near the Fermi energy and that the vertex correction due to impurity scattering vanishes. We therefore argue that the large spin Hall effect observed experimentally in platinum is of intrinsic nature.Comment: Accepted for publication in Phys. Rev. Let

Non-Commutative Tools for Topological Insulators

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have non-trivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.Comment: Final version (some arguments were corrected

Generating high-order optical and spin harmonics from ferromagnetic monolayers

High-order harmonic generation (HHG) in solids has entered a new phase of intensive research, with envisioned band-structure mapping on an ultrashort time scale. This partly benefits from a flurry of new HHG materials discovered, but so far has missed an important group. HHG in magnetic materials should have profound impact on future magnetic storage technology advances. Here we introduce and demonstrate HHG in ferromagnetic monolayers. We find that HHG carries spin information and sensitively depends on the relativistic spin-orbit coupling; and if they are dispersed into the crystal momentum ${\bf k}$ space, harmonics originating from real transitions can be ${\bf k}$-resolved and carry the band structure information. Geometrically, the HHG signal is sensitive to spatial orientations of monolayers. Different from the optical counterpart, the spin HHG, though probably weak, only appears at even orders, a consequence of SU(2) symmetry. Our findings open an unexplored frontier -- magneto-high-order harmonic generation.Comment: 19 pages, 4 figure

Anisotropic Decay Dynamics of Photoexcited Aligned Carbon Nanotube Bundles

We have performed polarization-dependent ultrafast pump-probe spectroscopy of a film of aligned single-walled carbon nanotube bundles. By taking into account imperfect nanotube alignment as well as anisotropic absorption cross sections, we quantitatively determined distinctly different photo-bleaching dynamics for polarizations parallel and perpendicular to the tube axis. For perpendicular polarization, we observe a slow (1.0-1.5 ps) relaxation process, previously unobserved in randomly-oriented nanotube bundles. We attribute this slower dynamics to the excitation and relaxation of surface plasmons in the radial direction of the nanotube bundles.Comment: 4 pages, 3 figure

Spin-orbit lateral superlattices: energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum and spin density in energy bands are studied for the two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasimomentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have the components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of external electric field is predicted.Comment: 6 pages, 5 figures, reported at the International Conferences "Nanophysics and Nanoelectronics" (Nizhny Novgorod, Russia, March 2006) and "Nanostructures: Physics and Technology" (St Petersburg, Russia, June 2006

Spin Hall effect of conserved current: Conditions for a nonzero spin Hall current

We study the spin Hall effect taking into account the impurity scattering effect as general as possible with the focus on the definition of the spin current. The conserved bulk spin current (Shi et al. [Phys. Rev. Lett. 96, 076604 (2006)]) satisfying the continuity equation of spin is considered in addition to the conventional one defined by the symmetric product of the spin and velocity operators. Conditions for non-zero spin Hall current are clarified. In particular, it is found that (i) the spin Hall current is non-zero in the Rashba model with a finite-range impurity potential, and (ii) the spin Hall current vanishes in the cubic Rashba model with a $\delta$-function impurity potential.Comment: 5 pages, minor change from the previous versio

Graphitic-BN Based Metal-free Molecular Magnets From A First Principle Study

We perform a first principle calculation on the electronic properties of carbon doped graphitic boron nitride graphitic BN. It was found that carbon substitution for either boron or nitrogen atom in graphitic BN can induce spontaneous magnetization. Calculations based on density functional theory with the local spin density approximation on the electronic band structure revealed a spin polarized, dispersionless band near the Fermi energy. Spin density contours showed that the magnetization density originates from the carbon atom. The magnetization can be attributed to the carbon 2p electron. Charge density distribution shows that the carbon atom forms covalent bonds with its three nearest neighbourhood. The spontaneous magnetization survives the curvature effect in BN nanotubes, suggesting the possibility of molecular magnets made from BN. Compared to other theoretical models of light-element or metal-free magnetic materials, the carbon-doped BN are more experimentally accessible and can be potentially useful.Comment: 8 pages, 4 figure