Crossover and coexistence of quasiparticle excitations in the fractional quantum hall regime at nu < or =1/3

New low-lying excitations are observed by inelastic light scattering at filling factors nu=p/(phip+/-1) of the fractional quantum Hall regime with phi=4. Coexisting with these modes throughout the range nu < or =1/3 are phi=2 excitations seen at 1/3. Both phi=2 and phi=4 excitations have distinct behaviors with temperature and filling factor. The abrupt first appearance of the new modes in the low-energy excitation spectrum at nu > or near 1/3 suggests a marked change in the quantum ground state on crossing the phi=2-->phi=4 boundary at nu=1/3.     

Coexistence of composite bosons and composite fermions in nu = 1/2 + 1/2 quantum Hall bilayers

In bilayer quantum Hall systems at filling fractions near nu=1/2+1/2, as the spacing d between the layers is continuously decreased, intralayer correlations must be replaced by interlayer correlations, and the composite fermion (CF) Fermi seas at large d must eventually be replaced by a composite boson (CB) condensate or "111 state" at small d. We propose a scenario where CBs and CFs coexist in two interpenetrating fluids in the transition. Trial wave functions describing these mixed CB-CF states compare very favorably with exact diagonalization results. A Chern-Simons transport theory is constructed that is compatible with experiment.     

Spin-liquid phase in a spin-1/2 quantum magnet on the kagome lattice

We study a model of hard-core bosons with short-range repulsive interactions at half filling on the kagome lattice. Using quantum Monte Carlo numerics, we find that this model shows a continuous superfluid-insulator quantum phase transition, with exponents z=1 and nu approximately 0.67(5). The insulator, I*, exhibits short-ranged density and bond correlations, topological order, and exponentially decaying spatial vison correlations, all of which point to a Z2 fractionalized phase. We estimate the vison gap in I* from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and S=1/2 spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/2 model with no special conservation laws.     

Criticality in the (2+1)-dimensional compact Higgs model and fractionalized insulators

We use a novel method of computing the third moment M3 of the action of the (2+1)-dimensional compact Higgs model in the adjoint representation with q=2 to extract correlation length and specific heat exponents nu and alpha without invoking hyperscaling. Finite-size scaling analysis of M3 yields the ratios (1+alpha)/nu and 1/nu separately. We find that alpha and nu vary along the critical line of the theory, which however exhibits a remarkable resilience of Z2 criticality. We propose this novel universality class to be that of the quantum phase transition from a Mott-Hubbard insulator to a charge-fractionalized insulator in two spatial dimensions.     

High-Resolution Absorption Spectroscopy of the 3nu(1) and 3nu(1) + nu(3) Bands of Propyne

The 3nu(1) and 3nu(1) + nu(3) bands of propyne have been recorded at Doppler-limited resolution by Fourier transform spectroscopy and intracavity laser absorption spectroscopy, respectively. The two bands show a mostly unperturbed J rotational structure for each individual K subband. However, as a rule the K structure ordering is perturbed in overtone transitions of propyne and different effective parameters associated with each K subband have been determined. From the vibrational energy levels, a value of -6.6 cm(-1) has been obtained for the x(13) cross anharmonicity in perfect agreement with the origins of the nu(1) + nu(3) and 2nu(1) + nu(3) combination bands estimated from the FTIR spectrum. Hot bands from the v(9) = 1 and v(10) = 1 levels associated with the 3nu(1) + nu(3) combination band have been partly rotationally analyzed and the retrieved values of x(39) and x(3,10) are in good agreement with literature values. Finally, the 4nu(1) + nu(9) - nu(9) band centered at 12 636.6 cm(-1) has been recorded by ICLAS. The red shift of this hot band relative to 4nu(1) and the DeltaB(v) value are discussed in relation to the anharmonic interaction between the 4nu(1) and 3nu(1) + nu(3) + nu(5) levels. Copyright 2000 Academic Press.     

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.     

Spin texture and magnetoroton excitations at nu=1/3

Neutral spin texture (ST) excitations at nu=1/3 are directly observed for the first time by resonant inelastic light scattering. They are determined to involve two simultaneous spin flips. At low magnetic fields, the ST energy is below that of the magnetoroton minimum. With increasing in-plane magnetic field these mode energies cross at a critical ratio of the Zeeman and Coulomb energies of eta(c)=0.020+/-0.001. Surprisingly, the intensity of the ST mode grows with temperature in the range in which the magnetoroton modes collapse. The temperature dependence is interpreted in terms of a competition between coexisting phases supporting different excitations. We consider the role of the ST excitations in activated transport at nu=1/3.     

Semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality d. The critical exponent nu controlling the divergence of the localization length at the transition is found to be nu=1/2+1/d-2 thus confirming that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality. Our analytical findings are in agreement with previous numerical results.     

Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.     

Paired composite fermion phase of quantum Hall bilayers at nu=1/2+1/2

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling nu=1/2+1/2 for intermediate spacing between the layers. We identify the phase as p_(x)+ip_(y) pairing, and construct high accuracy trial wave functions to describe the ground state on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes.     

Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

In this work, we investigate the accuracy of controlling spin I=1, 3/2 and 5/2 spin systems by average Hamiltonian theory. By way of example, we consider a simple two-pulse echo sequence and compare this perturbation scheme to a numerical solution of the Von Neumann equation. For the different values of I, we examine this precision as a function of the quadrupolar coupling as well as various experimental parameters such as the pulse spacing and pulse width. Experiments and simulations on I=3/2 and I=5/2 spin systems are presented that highlight a spectral artifact introduced due to finite pulse widths as predicted by average Hamiltonian theory. The control of these spin systems by this perturbation scheme is considered by investigating a phase cycling scheme that suppresses these artifacts to zeroth-order of the Magnus expansion.     

Mesoscopic fluctuations of the Coulomb drag at nu = 1/2

We consider mesoscopic fluctuations of Coulomb drag transresistivity between two layers at a Landau level filling factor nu = 1/2 each. We find that, at low temperatures, sample to sample fluctuations exceed both the ensemble average and the corresponding fluctuations at B = 0. At the experimentally relevant temperatures, the variance of the transresistivity is proportional to T(-1/2). We find the dependence of this variance on density and magnetic field to reflect the attachment of two flux quanta to each electron.     

Exact results for quench dynamics and defect production in a two-dimensional model

We show that for a d-dimensional model in which a quench with a rate tau(-1) takes the system across a (d-m)-dimensional critical surface, the defect density scales as n approximately 1/tau(mnu/(znu+1)), where nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d = 2 and m = nu = z = 1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model that can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.     

Evolving dark energy with w not = -1

Theories of evolving quintessence are constructed that generically lead to deviations from the w = -1 prediction of nonevolving dark energy. The small mass scale that governs evolution, m(phi) approximately = 10(-33) eV, is radiatively stable, and the "Why now?" problem is solved. These results rest on seesaw cosmology: Fundamental physics and cosmology can be broadly understood from only two mass scales, the weak scale nu and the Planck scale M. Requiring a scale of dark energy rho(DE)(1/4) governed by nu2/M and a radiatively stable evolution rate m(phi) given by nu4/M3 leads to a distinctive form for the equation of state w(z). Dark energy resides in the potential of a hidden axion field that is generated by a new QCD-like force that gets strong at the scale lambda approximately = nu2/M approximately = rho(DE)(1/4). The evolution rate is given by a second seesaw that leads to the axion mass m(phi) approximately = lambda2/f, with f approximately = M.     

Theoretical Study of the Collision-Induced Double Transition CO(2) (nu(3) = 1) + N(2) (nu(1) = 1) <-- CO(2) (nu(3) = 0) + N(2) (nu(1) = 0) at 296 K

A procedure is presented for the calculation of the double vibrational collision-induced absorption CO(2) (nu(3) = 1) + N(2) (nu(1) = 1) <-- CO(2) (nu(3) = 0) + N(2) (nu(1) = 0) on the basis of quantum lineshapes computed using an isotropic potential and dipole-induced dipole functions. The linestrengths and energies of the vibration-rotation transitions are treated explicitly for N(2), utilizing the HITRAN database for CO(2). The theoretical absorption profile is compared to recent experimental results. By narrowing the width of the individual lines contributing to the overall absorption profile relative to their values determined for N(2)-N(2) collision-induced absorption, excellent agreement between theory and experiment is obtained. Copyright 2000 Academic Press.     

High-Resolution Fourier Transform Spectra of HDSe: The Interacting States (v(1) v(2) v(3))/(v(1) +/- 1 v(2) -/+ 2 v(3)) with 2v(1) + v(2) = 1, 2, 3, and 4

For the first time, high-resolution Fourier transform spectra of HDSe in the region of the three polyads, nu(1)/2nu(2), nu(1) + nu(2)/3nu(2), and 2nu(1)/nu(1) + 2nu(2)/nu(2) + nu(3), have been recorded and analyzed. Combined with an earlier investigation of the nu(2) band, and including estimates for the unobserved "dark" 4nu(2) band, these levels were subjected to a "Global Fit," which makes use of relations between parameters within the different polyads. Since there are five isotopic species present in natural HD(M)Se (M = 82, 80, 78, 77, 76), altogether 34 vibration-rotation bands have been studied in the present contribution. The parameters determined by the Global Fit reproduce upper vibrational-rotational energies of all these bands with accuracies close to experimental precision. Copyright 2000 Academic Press.     

Microwave resonance of the bubble phases in 1/4 and 3/4 filled high Landau levels

We have measured the diagonal conductivity, sigma(xx), in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma(xx)] versus frequency when nu>4 and the partial filling of the highest Landau level, nu(*), is approximately 1/4 or 3/4 and temperatures <0.1 K. The resonance appears for a range of nu(*) from 0.20 to 0.38 and again from 0.64 to 0.80. The peak frequency f(pk) changes from approximately 500 to approximately 150 MHz as nu(*)=1/2 is approached. This range of f(pk) shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at about nu(*)=0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.     

Evolution of quasiparticle charge in the fractional quantum hall regime

The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the nu = 1/3 FQH state, a charge smoothly evolving from e(*) = e/3 for t(1/3) congruent with 1 to e(*) = e for t(1/3)<1 was determined, agreeing with chiral Luttinger liquid theory. In the nu = 2/5 FQH state the quasiparticle charge evolves smoothly from e(*) = e/5 at t(2/5) congruent with 1 to a maximum charge less than e(*) = e/3 at t(2/5)<1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.     

Naturally small seesaw neutrino mass with no new physics beyond the TeV scale

If there is no new physics beyond the TeV energy scale, such as in a theory of large extra dimensions, the smallness of the seesaw neutrino mass, i.e., m(nu) = m(2)(D)/m(N), cannot be explained by a very large m(N). In contrast to previous attempts to find an alternative mechanism for a small m(nu), I show how a solution may be obtained in a simple extension of the standard model, without using any ingredient supplied by the large extra dimensions. It is also experimentally testable at future accelerators.     

New phase transition between partially and fully polarized quantum Hall states with charge and spin gaps at nu = 2/3

The average electron spin polarization Rho of a two-dimensional electron gas confined in GaAs/GaAlAs multiple quantum wells was measured by NMR near the fractional quantum Hall state with filling factor nu = 2/3. Above this filling factor (2/3< or = nu < 0.85), a strong depolarization is observed corresponding to two spin flips per additional flux quantum. The most remarkable behavior of the polarization is observed at nu = 2/3, where a quantum phase transition from a partially polarized (Rho approximately 3/4) to a fully polarized (Rho = 1) state can be driven by increasing the ratio between the Zeeman and the Coulomb energy above a critical value eta(c) = Delta(Z)/Delta(C) = 0.0185.