Showing papers by "Eugene J. Mele published in 2007"
TL;DR: In this paper, the authors studied three-dimensional generalizations of the quantum spin Hall (QSH) effect and introduced a tight binding model which realized the WTI and STI phases, and discussed its relevance to real materials including bismuth.
Abstract: We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single ${Z}_{2}$ 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 destroyed by disorder. The STI are robust and lead to novel ``topological metal'' surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.
3,357 citations
Journal Article•
TL;DR: A tight binding model is introduced which realizes the WTI and STI phases, and its relevance to real materials, including bismuth is discussed.
Abstract: We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single ${Z}_{2}$ 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 destroyed by disorder. The STI are robust and lead to novel ``topological metal'' surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.
2,325 citations
TL;DR: In this article, the location of the release point of a particle that slides on the surface of a frictionless sphere when it is released from rest at the top is studied. And the authors generalize this problem to include the effects of sliding friction and solve it by a perturbation expansion in the coefficient of friction.
Abstract: A well studied problem in elementary mechanics is the location of the release point of a particle that slides on the surface of a frictionless sphere when it is released from rest at the top. We generalize this problem to include the effects of sliding friction and solve it by a perturbation expansion in the coefficient of sliding friction and by an exact integration of the equation of motion. A comparison of the two solutions identifies a parameter range where the perturbation series accurately represents the motion of the particle and another range where the perturbative solution fails qualitatively to describe the motion of the particle.
19 citations
TL;DR: In this article, the effect of a spatially localized transverse electric field on the low-energy electronic structure of semiconducting carbon nanotubes has been studied, and the binding energy of these subgap states as a function of the range and strength of the electrostatic potential has been analyzed.
Abstract: We introduce two simple models to study the effect of a spatially localized transverse electric field on the low-energy electronic structure of semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the low-energy states of a carbon nanotube, we use scattering theory to show that an arbitrarily weak field leads to the formation of localized electronic states inside the free nanotube band gap. We study the binding energy of these subgap states as a function of the range and strength of the electrostatic potential. When the range of the potential is held constant and the strength is varied, the binding energy shows crossover behavior: the states lie close to the free nanotube band edge until the potential exceeds a threshold value, after which the binding energy increases rapidly. When the potential strength is held constant and the range is varied, we find resonant behavior: the binding energy passes through a maximum as the range of the potential is increased. Large electric fields confined to a small region of the nanotube are required to create localized states far from the band edge.
4 citations
TL;DR: In this paper, the authors developed and solved a continuum theory for the piezoelectric response of nanotubes under applied uniaxial and torsional stresses and found that the response is controlled by the chiral angle, the aspect ratio, and two dimensionless parameters specifying the ratio of the strengths of the electrostatic and elastic energies.
Abstract: We develop and solve a continuum theory for the piezoelectric response of nanotubes under applied uniaxial and torsional stresses. We find that the piezoelectric response is controlled by the chiral angle, the aspect ratio, and two dimensionless parameters specifying the ratio of the strengths of the electrostatic and elastic energies. The model is solved in two limiting cases and the solutions are discussed. These systems are found to have several unexpected physical effects not seen in conventional bulk systems, including a strong stretch-twist coupling and the development of a significant bound charge density in addition to a surface charge density. The model is applied to estimate the piezoelectric response of a boron nitride nanotube under uniform tensile stress.
3 citations