Topological winding properties of spin edge states in Kane-Mele graphene model

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].Comment: 9 pages, 10 figure

Topological phases and fractional excitations of the exciton condensate in a special class of bilayer systems

We study the exciton condensate in zero temperature limit in a special class of electron-hole bilayer systems adjacent to insulating ferromagnetic films. With the self-consistent mean-field approximation, we find that the Rashba spin-orbit interaction in the electron and hole layers can induce the p \pm ip or p pairing states depending on the different magnetization of the overlapped ferromagnetic films. Correspondingly, the topologically nontrivial or trivial phases emerge. Furthermore, in the topologically nontrivial phase, the quasiparticle excitations of the U(1) vortex are attached to fractional quantum numbers and obey Abelian statistics.Comment: 7 pages, 5 figure

Quantum Hall Effects in a Non-Abelian Honeycomb Lattice

We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall effects in honeycomb optical lattice when the internal valley degrees of freedom enlarge.Comment: 7 pages, 6 figure