Thermal fluctuations and anomalous elasticity of homogeneous nematic elastomers

We present a unified formulation of a rotationally invariant nonlinear elasticity for a variety of spontaneously anisotropic phases, and use it to study thermal fluctuations in nematic elastomers and spontaneously anisotropic gels. We find that in a thermodynamic limit homogeneous nematic elastomers are universally incompressible, are characterized by a universal ratio of shear moduli, and exhibit an anomalous elasticity controlled by a nontrivial low temperature fixed point perturbative in D=3-epsilon dimensions. In three dimensions, we make predictions that are asymptotically exact.Comment: 4 RevTeX pgs,,submitted to Europhysics Letter

Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators

We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating on-site energies on the AB sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from that either in traditional QHE systems or in graphene.Comment: 4 pages, 4 figure

A topological look at the quantum spin Hall state

We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the former scenario generally resulting in counterpropagating gapless edge states. Based upon the Kane-Mele model with a uniform exchange field and a sublattice staggered confining potential near the sample boundaries, we demonstrate the existence of such gapless edge states and their robust properties in the presence of impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.Comment: 5 pages, 4 figure

Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic (FM) region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the FM region, and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes", the QSH effect becomes robust against symmetry-breaking perturbations.Comment: 5 pages, 4 figure

Time-reversal-symmetry-broken quantum spin Hall effect

Quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers $C_{\pm}=\pm 1$ persists when the TR symmetry is broken. A topological phase transition from the TR symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR symmetry-broken QSH phase to an ordinary insulator state can not happen without closing the band gap.Comment: 5 pages, 5 figure