Nonlocal Edge State Transport in Topological Insulators

We use the N-terminal scheme for studying the edge state transportin in two-dimensional topological insulators. We find the universal nonlocal response in the ballistic transport approach. This macroscopic exhibition of the topological order offers different areas for applications.Comment: Updated to published versio

Universal properties of materials with Dirac dispersion relation of low-energy excitations

The N-terminal scheme is considered for studying the contribution of edge states to the response of a two-dimensional topological insulator. A universal distribution of the nonlocal resistance between terminals is determined in the ballistic transport approach. The calculated responses are identical to experimentally observed values. The spectral properties of surface electronic states in Weyl semimetals are also studied. The density of surface states is accurately determined. The universal behavior of these characteristics is a distinctive feature of the considered Dirac materials which can be used in practical applications

Topological phase states of the SU(3) QCD

We consider the topologically nontrivial phase states and the corresponding topological defects in the SU(3) d-dimensional quantum chromodynamics (QCD). The homotopy groups for topological classes of such defects are calculated explicitly. We have shown that the three nontrivial groups are pi_3 SU(3)=Z, pi_5 SU(3)=Z, and pi_6 SU(3)=Z_6 if 3 < d < 6. The latter result means that we are dealing exactly with six topologically different phase states. The topological invariants for d=3,5,6 are described in detail.Comment: LATEX2e, 5 page

Unoccupied Topological States on Bismuth Chalcogenides

The unoccupied part of the band structure of topological insulators Bi$_2$Te$_{x}$Se$_{3-x}$ ($x=0,2,3$) is studied by angle-resolved two-photon photoemission and density functional theory. For all surfaces linearly-dispersing surface states are found at the center of the surface Brillouin zone at energies around 1.3 eV above the Fermi level. Theoretical analysis shows that this feature appears in a spin-orbit-interaction induced and inverted local energy gap. This inversion is insensitive to variation of electronic and structural parameters in Bi$_2$Se$_3$ and Bi$_2$Te$_2$Se. In Bi$_2$Te$_3$ small structural variations can change the character of the local energy gap depending on which an unoccupied Dirac state does or does not exist. Circular dichroism measurements confirm the expected spin texture. From these findings we assign the observed state to an unoccupied topological surface state

Universal properties of materials with Dirac dispersion relation of low-energy excitations

The N-terminal scheme is considered for studying the contribution of edge states to the response of a two-dimensional topological insulator. A universal distribution of the nonlocal resistance between terminals is determined in the ballistic transport approach. The calculated responses are identical to experimentally observed values. The spectral properties of surface electronic states in Weyl semimetals are also studied. The density of surface states is accurately determined. The universal behavior of these characteristics is a distinctive feature of the considered Dirac materials which can be used in practical applications