Quantized Transport in Two-Dimensional Spin-Ordered Structures

We study in detail the transport properties of a model of conducting electrons in the presence of double-exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami, and Nagaosa (2000). The relationship between the canting angle of the spin texture $\theta$ and the Berry phase field flux per triangular plaquette $\phi$ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect (Haldane, 1988). The quantization of the transverse (Hall) conductivity $\sigma_{xy}$ is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity $\sigma_{xx}$ shows the existence of a metal-insulator transition as a function of the canting angle $\theta$ (or flux density $\phi$). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.Comment: 17 pages, 12 figure

String and membrane condensation on three-dimensional lattices

In this paper, we investigate the general properties of lattice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three three-dimensional spin models which lead to Z(2) gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first model contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a different type of topological order

Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure

We generalize the topological entanglement entropy to a family of topological Reacutenyi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Reacutenyi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum

Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.Comment: 4+ pages, 3 figure

Fractional quantum Hall effect in the absence of Landau levels

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the FQHE in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically nontrivial flat band model on the checkerboard lattice \cite{sun}. In the presence of nearest-neighboring repulsion ($U$), we find that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5 filling, however, a next-nearest-neighboring repulsion is needed for the occurrence of the 1/5 FQHE when $U$ is not too strong. We demonstrate the characteristic features of these novel states and determine the phase diagram correspondingly.Comment: 6 pages and 4 figure

Topologically protected quantum bits from Josephson junction arrays

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation, while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev, holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Comment: 6 pages, 4 figure

Local Thermometry of Neutral Modes on the Quantum Hall Edge

A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.Comment: 24 pages, 18 figure

Abrupt Onset of Second Energy Gap at Superconducting Transition of Underdoped Bi2212

The superconducting gap - an energy scale tied to the superconducting phenomena-opens on the Fermi surface at the superconducting transition temperature (TC) in conventional BCS superconductors. Quite differently, in underdoped high-TC superconducting cuprates, a pseudogap, whose relation to the superconducting gap remains a mystery, develops well above TC. Whether the pseudogap is a distinct phenomenon or the incoherent continuation of the superconducting gap above TC is one of the central questions in high-TC research. While some experimental evidence suggests they are distinct, this issue is still under intense debate. A crucial piece of evidence to firmly establish this two-gap picture is still missing: a direct and unambiguous observation of a single-particle gap tied to the superconducting transition as function of temperature. Here we report the discovery of such an energy gap in underdoped Bi2212 in the momentum space region overlooked in previous measurements. Near the diagonal of Cu-O bond direction (nodal direction), we found a gap which opens at TC and exhibits a canonical (BCS-like) temperature dependence accompanied by the appearance of the so-called Bogoliubov quasiparticles, a classical signature of superconductivity. This is in sharp contrast to the pseudogap near the Cu-O bond direction (antinodal region) measured in earlier experiments. The emerging two-gap phenomenon points to a picture of richer quantum configurations in high temperature superconductors.Comment: 16 pages, 4 figures, authors' version Corrected typos in the abstrac

Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene

The quantum-Hall-effect (QHE) occurs in topologically-ordered states of two-dimensional (2d) electron-systems in which an insulating bulk-state coexists with protected 1d conducting edge-states. Owing to a unique topologically imposed edge-bulk correspondence these edge-states are endowed with universal properties such as fractionally-charged quasiparticles and interference-patterns, which make them indispensable components for QH-based quantum-computation and other applications. The precise edge-bulk correspondence, conjectured theoretically in the limit of sharp edges, is difficult to realize in conventional semiconductor-based electron systems where soft boundaries lead to edge-state reconstruction. Using scanning-tunneling microscopy and spectroscopy to follow the spatial evolution of bulk Landau-levels towards a zigzag edge of graphene supported above a graphite substrate we demonstrate that in this system it is possible to realize atomically sharp edges with no edge-state reconstruction. Our results single out graphene as a system where the edge-state structure can be controlled and the universal properties directly probed.Comment: 16 pages, 4 figure

Spin chirality on a two-dimensional frustrated lattice

The collective behavior of interacting magnetic moments can be strongly influenced by the topology of the underlying lattice. In geometrically frustrated spin systems, interesting chiral correlations may develop that are related to the spin arrangement on triangular plaquettes. We report a study of the spin chirality on a two-dimensional geometrically frustrated lattice. Our new chemical synthesis methods allow us to produce large single crystal samples of KFe3(OH)6(SO4)2, an ideal Kagome lattice antiferromagnet. Combined thermodynamic and neutron scattering measurements reveal that the phase transition to the ordered ground-state is unusual. At low temperatures, application of a magnetic field induces a transition between states with different non-trivial spin-textures.Comment: 7 pages, 4 figure