Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to… Expand

Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and 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.Expand

The Z2 order of the QSH phase is established in the two band model of graphene and a generalization of the formalism applicable to multiband and interacting systems is proposed.Expand

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$… Expand

We introduce and analyze a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define a ``${Z}_{2}$ pump.'' For an isolated system, a… Expand

It is shown that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.Expand

A theory of the long-wavelength low-energy electronic structure of graphite-derived nanotubules is presented. The propagating {pi} electrons are described by wrapping a massless two dimensional Dirac… Expand

The mathematical connection between isostatic lattices—which are relevant for granular matter, glasses and other ‘soft’ systems—and topological quantum matter is as deep as it is unexpected.