Paleogeographic, Paleoceanographic, and Tectonic Controls on Early Late Ordovician Graptolite Diversity Patterns

The Katian Age (early Late Ordovician) was a time of significant decline in marine biodiversity, but whether this decline was a real phenomenon or an artifact of the relatively few studies devoted to this interval requires further research. We examined the pattern of graptolite faunal changes across the boundary between the Climacograptus bicornis and Diplacanthograptus caudatus graptolite zones in North America and on several other continents. A sharp decline in species diversity occurs in the Appalachian Basin. Scores for normalized diversity dropped from 20 in the C. bicornis Zone to 7 in the D. caudatus Zone. Only 11% of the species present in the C. bicornis Zone carry over into the D. caudatus Zone. A similar pattern occurs in central Oklahoma. Regions at higher paleolatitude, such as Wales and Baltoscandia, exhibit low graptolite diversity in lower Katian strata, and then diversity declines further in higher strata. In other regions at low paleolatitude, such as Australasia and Scotland, however, diversity is fairly constant across this interval (although the percentage of carryover taxa remains low). We conclude that seawater temperature change or disruption of the oceanic density structure, which might accompany temperature change, provides explanations for the similarity between Laurentian and higher paleolatitude diversity patterns. Flooding of the Laurentian craton through the Sebree Trough by cool, subpolar Iapetus seawater may have adversely affected graptolite diversity there. Regions at high paleolatitudes likely underwent cooling associated with Katian climate deterioration. Thus seawater cooling, albeit driven by different mechanisms, may have produced similar diversity patterns at different paleolatitudes

Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms

We propose a scheme to implement Kitaev's honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum simulators. We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom. We address the challenge of probing the physics of Majorana fermions, while having only access to the original composite spin degrees of freedom. Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive. The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically-prepared states. By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators

Electronic localization in two dimensions

By an improved scaling analysis, we suggest that there may appear two possibilities concerning the electronic localization in two dimensional random media. The first is that all electronic states are localized in two dimensions, as already conjectured previously. The second possibility is that the electronic behaviors in two and three dimensional random systems are similar, in agreement with a recent calculation based on a direct calculation of the conductance with the use of the Kubo formula. In this case, non-localized states is possible in two dimensions, and possess some peculiar properties. A few predictions are proposed. Moreover, the present analysis seems accommodating results from previous scaling analysis.Comment: 6 pages, 2 figure

Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set

Stress evolution in GaAsN alloy films

We have investigated stress evolution in dilute nitride GaAs1−xNxGaAs1−xNx alloy films grown by plasma-assisted molecular-beam epitaxy. For coherently strained films (x2.5%x>2.5%, in situ wafer curvature measurements reveal a signature for stress relaxation. Atomic force microscopy and transmission electron microscopy measurements indicate that stress relaxation occurs by a combination of elastic relaxation via island formation and plastic relaxation associated with the formation of stacking faults.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87566/2/103523_1.pd

Matrix-seeded growth of nitride semiconductor nanostructures using ion beams

We have examined the matrix-seeded growth of narrow-gap nitride nanostructures in nitrogen ion implanted GaAs and InAs. Low-energy implantation followed by rapid thermal annealing (RTA) results in the formation of 2–3 nm sized amorphous precipitates in a crystalline matrix. On the other hand, high-energy implantation results in an amorphous layer, with or without crystalline remnants. When the ion-beam-synthesized amorphous matrix is a continuous amorphous layer, subsequent RTA leads to the formation of 4–5 nm zinc blende (ZB)-GaN-rich crystallites in an amorphous matrix. When this matrix contains crystalline remnants, subsequent RTA leads to the formation of 2–4 nm ZB-GaN-rich crystallites within the amorphous regions. These results suggest that the matrix plays an important role in the nucleation and growth of narrow-gap nitride nanostructures, and that matrix-seeded growth may provide an opportunity to control the structure and properties of the nanostructures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87633/2/064301_1.pd

Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump

The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example thereof is the two-dimensional integer quantum Hall effect. It is characterized by the first Chern number which manifests in the quantized Hall response induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional systems leads to the appearance of a novel non-linear Hall response that is quantized as well, but described by a 4D topological invariant - the second Chern number. Here, we report on the first observation of a bulk response with intrinsic 4D topology and the measurement of the associated second Chern number. By implementing a 2D topological charge pump with ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small atom cloud as a local probe, we fully characterize the non-linear response of the system by in-situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probe higher-dimensional quantum Hall systems, where new topological phases with exotic excitations are predicted

Topological phase transitions in the non-Abelian honeycomb lattice

Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics can be tested. Here, we generalize this system to non-Abelian quantum electrodynamics, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly-interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.Comment: RevTex4 file, color figure

Gauge fields for ultracold atoms in optical superlattices

We present a scheme that produces a strong U(1)-like gauge field on cold atoms confined in a two-dimensional square optical lattice. Our proposal relies on two essential features, a long-lived metastable excited state that exists for alkaline-earth or Ytterbium atoms, and an optical superlattice. As in the proposal by Jaksch and Zoller [New Journal of Physics 5, 56 (2003)], laser-assisted tunneling between adjacent sites creates an effective magnetic field. In the tight-binding approximation, the atomic motion is described by the Harper Hamiltonian, with a flux across each lattice plaquette that can realistically take any value between 0 and $\pi$. We show how to take advantage of the superlattice to ensure that each plaquette acquires the same phase, thus simulating a uniform magnetic field. We discuss the observable consequences of the artificial gauge field on non-interacting bosonic and fermionic gases. We also outline how the scheme can be generalized to non-Abelian gauge fields

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.Comment: RevTex, 4 pages, 1 ps figur