On conformally flat circle bundles over surfaces

We study surface groups $\Gamma$ in $SO(4,1)$, which is the group of Mobius tranformations of $S^3$, and also the group of isometries of $\mathbb{H}^4$. We consider such $\Gamma$ so that its limit set $\Lambda_\Gamma$ is a quasi-circle in $S^3$, and so that the quotient $(S^3 - \Lambda_\Gamma) / \Gamma$ is a circle bundle over a surface. This circle bundle is said to be conformally flat, and our main goal is to discover how twisted such bundle may be by establishing a bound on its Euler number. By combinatorial approaches, we have two soft bounds in this direction on certain types of nice structures. In this article we also construct new examples, a "grafting" type path in the space of surface group representations into $SO(4,1)$: starting inside the quasi-Fuschsian locus, going through non-discrete territory and back.Comment: 28 pages, 7 figures. Updated from Thesis version: more correct bound of (3/2)n^2, updated exposition in section 3.

Commuting-projector Hamiltonians for chiral topological phases built from parafermions

We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve $\mathbb{Z}_{3}$ parafermion zero modes residing in a parent fractional-quantum-Hall fluid. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which $\mathbb{Z}_2$ spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced $\mathbb{Z}_3$ parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with $\text{SU}(2)_{4}$ topological order, and can be accessed by gauging the $\mathbb{Z}_{2}$ symmetry in the SET. Employing Levin-Wen string-net models with $\mathbb{Z}_{2}$-graded structure, we generalize this picture to construct a large class of commuting-projector models for $\mathbb{Z}_{2}$ SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order.Comment: 29+18 pages, 25 figure

Formation of high-quality Ag-based ohmic contacts to p-type GaN

Low resistance and high reflectance ohmic contacts on p-type GaN were achieved using an Ag-based metallization scheme. Oxidation annealing was the key to achieve ohmic behavior of Ag-based contacts on p-type GaN. A low contact resistivity of similar to 5x10(-5) Omega cm(2) could be achieved from Me (=Ni, Ir, Pt, or Ru)/Ag (50/1200 angstrom) contacts after annealing at 500 degrees C for 1 min in O(2) ambient. Oxidation annealing promoted the out-diffusion of Ga atoms from the GaN layer, and Ga atoms dissolved in the in-diffused Ag layer with the formation of Ag-Ga solid solution, resulting in ohmic contact formation. Using Ru/Ni/Au (500/200/500 angstrom) overlayers on the Me/Ag contacts, the excessive incorporation of oxygen molecules into the contact interfacial region, and the out-diffusion and agglomeration of Ag, were effectively prevented during oxidation annealing. As a result, a high reflectance of 87.2% at the 460 nm wavelength and a smooth surface morphology could be obtained simultaneously. (C) 2008 The Electrochemical Society.open111618sciescopu

The Eco-School Project at the Daegu National University of Education

Asia Education Symposium 2006, Session 3: “Making the most of Resources of International Education”( Day Two; Sun., October 16

Spin force and intrinsic spin Hall effect in spintronics systems

We investigate the spin Hall effect (SHE) in a wide class of spin-orbit coupling systems by using spin force picture. We derive the general relation equation between spin force and spin current and show that the longitudinal force component can induce a spin Hall current, from which we reproduce the spin Hall conductivity obtained previously using Kubo's formula. This simple spin force picture gives a clear and intuitive explanation for SHE