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

Commuting-projector Hamiltonians for two-dimensional topological insulators: Edge physics and many-body invariants

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Z. Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that describes an interacting yet exactly solvable 2D topological insulator. We explicitly show that both the gapped and gapless boundaries of our model are consistent with those of band-theoretic, weakly interacting topological insulators. Interestingly, on certain lattices our time-reversal-symmetric models also enjoy CP symmetry, leading to intuitive interpretations of the bulk invariant for a CP-symmetric topological insulator upon putting the system on a Klein bottle. We also briefly discuss how these many-body invariants may be able to characterize models with only time-reversal symmetry

Ising Anyons in Frustration-Free Majorana-Dimer Models

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion