Gunnar Moller

Artificial square ice and related dipolar nanoarrays.

We study a frustrated dipolar array recently manufactured lithographically by Wang in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

Composite Fermion Theory for Bosonic Quantum Hall States on Lattices

We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.

Magnetic diffuse scattering in artificial kagome spin ice

Magnetic phases and phase transitions in artificial spin ice, constructed from tailor-made arrays of nanomagnets, are currently subjects of great interest. The authors present measurements of the diffuse soft x-ray resonant magnetic scattering in artificial spin ice, where the moments of the magnets, arranged on the sites of the kagome lattice, are highly dynamic. Comparing experimental scattering patterns with the patterns calculated from Monte Carlo simulations based on a needle-dipole model, they show the emergence of quasi-pinch-points in the kagome ice I phase, and explain their relation to the pinch-point singularities in spin ice pyrochlores. As in the bulk pyrochlore spin ices, measurement of diffuse scattering from artificial kagome spin ice provides unique information on the magnetic correlations and can be applied to a number of other problems concerning nanomagnetic systems.

Paired composite-fermion wave functions

We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.

Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number

The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number C. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with |C|>1. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor ν, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors ν=r/(r|C|+1) for bosons, or ν=r/(2r|C|+1) for fermions. This series includes a bosonic integer quantum Hall state in |C|=2 bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.

Majorana modes and p-wave superfluids for fermionic atoms in optical lattices

The quest for realization of non-Abelian phases of matter, driven by their possible use in fault-tolerant topological quantum computing, has been spearheaded by recent developments in p-wave superconductors. The chiral p(x)+ip(y)-wave superconductor in two-dimensions exhibiting Majorana modes provides the simplest phase supporting non-Abelian quasiparticles and can be seen as the blueprint of fractional topological order. Alternatively, Kitaevs Majorana wire has emerged as an ideal toy model to understand Majorana modes. Here we present a way to make the transition from Kitaevs Majorana wires to two-dimensional p-wave superconductors in a system with cold atomic gases in an optical lattice. The main idea is based on an approach to generate p-wave interactions by coupling orbital degrees of freedom with strong s-wave interactions. We demonstrate how this design can induce Majorana modes at edge dislocations in the optical lattice, and we provide an experimentally feasible protocol for the observation of the non-Abelian statistics.

Fractional quantum Hall effect of lattice bosons near commensurate flux.

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low-energy physics is mapped to a multispecies continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or pseudospin. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wave functions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wave functions can be destabilized when umklapp processes become strong.

Trial wave functions for ν = 1 2 + 1 2 quantum Hall bilayers

Quantum Hall bilayer systems at filling fractions near

Geometric stability of topological lattice phases.

\nu=\half+\half

Adiabatic continuation of fractional Chern insulators to fractional quantum Hall States.

undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation