Weak topological insulator with protected gapless helical states

A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap, when the surface is deformed into a cylinder penetrating the otherwise surface-less system. We show that when a dislocation with a non-trivial Burgers vector is introduced, the finite-size energy gap play the role of stabilizing the one-dimensional gapless states.Comment: 8 pages, 17 figure

Solvent Extraction of V(III, IV, V) with Acetylacetone

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Zigzag edge modes in Z2 topological insulator: reentrance and completely flat spectrum

The spectrum and wave function of helical edge modes in Z_2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a "mass" term M (k) that is parameterized as M (k) = Delta - B k^2. A topological insulator realizes when the parameters Delta and B fall on the regime, either 0 < Delta /B < 4 or 4 < Delta /B < 8. At Delta /B = 4, which separates the cases of positive and negative (quantized) spin Hall conductivities, the edge modes show a corresponding change that depends on the edge geometry. In the (1,0)-edge, the spectrum of edge mode remains the same against change of Delta /B, although the main location of the mode moves from the zone center for Delta /B < 4, to the zone boundary for Delta /B > 4 of the 1D Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Delta /B = 4 where the spectrum becomes independent of the momentum, i.e. flat, over the whole 1D Brillouin zone. Furthermore, for Delta/B < 1.354..., the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.Comment: 19 pages, 33 figure

Synergic Extraction of Rare Earth Elements with Thenoyltrifluoroacetone and Neutral Bidentate Ligands

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Substoichiometric Isotope Dilution Analysis of Vanadium by Synergistic Extraction

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Tunneling into fractional quantum Hall liquids

Motivated by the recent experiment by Grayson et.al., we investigate a non-ohmic current-voltage characteristics for the tunneling into fractional quantum Hall liquids. We give a possible explanation for the experiment in terms of the chiral Tomonaga-Luttinger liquid theory. We study the interaction between the charge and neutral modes, and found that the leading order correction to the exponent $\alpha$ $(I\sim V^\alpha)$ is of the order of $\sqrt{\epsilon}$ $(\epsilon=v_n/v_c)$, which reduces the exponent $\alpha$. We suggest that it could explain the systematic discrepancy between the observed exponents and the exact $\alpha =1/\nu$ dependence.Comment: Latex, 5 page

Solvent Extraction of Lanthanoid(III) with 18-Crown-6 and Trichloroacetate Ion

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Spin Berry phase in the Fermi arc states

Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its band dispersion exhibits multiple subbands of partially flat dispersion, originating from the Fermi arc states. Remarkably, the lowest energy flat subbands bear a finite size energy gap, implying that electrons in the Fermi arc surface states are susceptible of the spin Berry phase. This is shown to be a consequence of spin-to-surface locking in the surface electronic states. We verify this behavior and the existence of spin Berry phase in the low-energy effective theory of Fermi arc surface states on a cylindrical nanowire by deriving the latter from a bulk Weyl Hamiltonian. We point out that in any surface state exhibiting a spin Berry phase pi, a zero-energy bound state is formed along a magnetic flux tube of strength, hc/(2e). This effect is highlighted in a surfaceless bulk system pierced by a dislocation line, which shows a 1D chiral mode along the dislocation line.Comment: 9 pages, 9 figure

Anomalous tunneling conductances of a spin singlet \nu=2/3 edge states: Interplay of Zeeman splitting and Long Range Coulomb Interaction

The point contact tunneling conductance between edges of the spin singlet $\nu=2/3,\hat{K}=(3/3/0)$ quantum Hall states is studied both in the quasiparticle tunneling picture and in the electron tunneling picture. Due to the interplay of Zeeman splitting and the long range Coulomb interaction between edges of opposite chirality novel spin excitations emerge, and their effect is characterized by anomalous exponents of the charge and spin tunneling conductances in various temperature ranges. Depending on the kinds of scatterings at the point contact and the tunneling mechanism the anomalous interaction in spin sector may enhance or suppress the tunneling conductances. The effects of novel spin excitation are also relevant to the recent NMR experiments on quantum Hall edges.Comment: Revtex File, 7 pages: To be published in Physical Reviews