Electron Interactions and Scaling Relations for Optical Excitations in Carbon Nanotubes

Recent fluorescence spectroscopy experiments on single wall carbon nanotubes reveal substantial deviations of observed absorption and emission energies from predictions of noninteracting models of the electronic structure. Nonetheless, the data for nearly armchair nanotubes obey a nonlinear scaling relation as a function the tube radius $R$. We show that these effects can be understood in a theory of large radius tubes, derived from the theory of two dimensional graphene where the coulomb interaction leads to a logarithmic correction to the electronic self energy and marginal Fermi liquid behavior. Interactions on length scales larger than the tube circumference lead to strong self energy and excitonic effects that compete and nearly cancel so that the observed optical transitions are dominated by the graphene self energy effects.Comment: 4 page

Surface States of Topological Insulators

We develop an effective bulk model with a topological boundary condition to study the surface states of topological insulators. We find that the Dirac point energy, the band curvature and the spin texture of surface states are crystal face-dependent. For a given face on a sphere, the Dirac point energy is determined by the bulk physics that breaks p-h symmetry in the surface normal direction and is tunable by surface potentials that preserve T symmetry. Constant energy contours near the Dirac point are ellipses with spin textures that are helical on the S/N pole, collapsed to one dimension on any side face, and tilted out-of-plane otherwise. Our findings identify a route to engineering the Dirac point physics on the surfaces of real materials.Comment: 4.1 pages, 2 figures and 1 tabl

Quantum Spin Hall Effect in Graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.Comment: 4 pages, published versio

Z2Z_2 Topological Order and the Quantum Spin Hall Effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel $Z_2$ topological invariant, which distinguishes it from an ordinary insulator. The $Z_2$ classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the $Z_2$ order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multi band and interacting systems.Comment: 4 pages RevTeX. Added reference, minor correction

Spin texture on the Fermi surface of tensile strained HgTe

We present ab initio and k.p calculations of the spin texture on the Fermi surface of tensile strained HgTe, which is obtained by stretching the zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal with pointlike accidental degeneracies between a mirror symmetry protected twofold degenerate band and two nondegenerate bands near the Fermi level. The Fermi surface consists of two ellipsoids which contact at the point where the Fermi level crosses the twofold degenerate band along the (111) axis. However, the spin texture of occupied states indicates that neither ellipsoid carries a compensating Chern number. Consequently, the spin texture is locked in the plane perpendicular to the (111) axis, exhibits a nonzero winding number in that plane, and changes winding number from one end of the Fermi ellipsoids to the other. The change in the winding of the spin texture suggests the existence of singular points. An ordered alloy of HgTe with ZnTe has the same effect as stretching the zincblende lattice in the (111) direction. We present ab initio calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin texture locked in a 2D plane on the Fermi surface with different winding numbers on either end.Comment: 8 pages, 8 figure