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- Charles L . Kane, Eugene J. Mele
- Physical review letters
- 2005

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… (More)

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducted states on their edge or surface. These states are possible due to the combination of spinorbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a… (More)

- Liang Fu, Charles L . Kane, Eugene J. Mele
- Physical review letters
- 2007

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are… (More)

- Charles L . Kane, Eugene J. Mele
- Physical review letters
- 2005

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 Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time… (More)

Using low-resistance electrical contacts, we have measured the intrinsic high-field transport properties of metallic single-wall carbon nanotubes. Individual nanotubes appear to be able to carry currents with a density exceeding 109 A cm2. As the bias voltage is increased, the conductance drops dramatically due to scattering of electrons. We show that the… (More)

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 Z2 topological invariants, which characterize the ground state. In two dimensions, there is a single Z2 invariant that distinguishes the ordinary insulator from the… (More)

We introduce and analyze a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define a “Z2 pump.” For an isolated system, a single closed cycle of the pump changes the expectation value of the spin at each end even when spin-orbit interactions violate the conservation of spin. A second cycle,… (More)

- Liang Fu, Charles L . Kane
- Physical review letters
- 2008

We study the proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The resulting two-dimensional state resembles a spinless px+ipy superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors… (More)

We study junctions between superconductors mediated by the edge states of a quantum-spin-Hall insulator. We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4π rather than a 2π periodicity. This effect is a consequence of the conservation of fermion parity—the number of electron mod 2—in a… (More)

- Youngkuk Kim, Benjamin J Wieder, Charles L . Kane, Andrew M Rappe
- Physical review letters
- 2015

We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2… (More)