Ge growth on ion-irradiated Si self-affine fractal surfaces

We have carried out scanning tunneling microscopy experiments under ultrahigh vacuum condition to study the morphology of ultrathin Ge films eposited on pristine Si(100) and ion-irradiated Si(100) self-affine fractal surfaces. The pristine and the ion-irradiated Si(100) surface have roughness exponents of alpha=0.19+/-0.05 and alpha=0.82+/-0.04 respectively. These measurements were carried out on two halves of the same sample where only one half was ion-irradiated. Following deposition of a thin film of Ge (~6 A) the roughness exponents change to 0.11+/-0.04 and 0.99+/-0.06, respectively. Upon Ge deposition, while the roughness increases by more than an order of magnitude on the pristine surface, a smoothing is observed for the ion-irradiated surface. For the ion-irradiated surface the correlation length xi increases from 32 nm to 137 nm upon Ge deposition. Ge grows on Si surfaces in the Stranski-Krastanov or layer-plus-island mode where islands grow on a wetting layer of about three atomic layers. On the pristine surface the islands are predominantly of square or rectangular shape, while on the ion-irradiated surface the islands are nearly diamond shaped. Changes of adsorption behaviour of deposited atoms depending on the roughness exponent (or the fractal dimension) of the substrate surface are discussed.Comment: 5 pages, 2 figures and 1 tabl

Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-TcT_{c} superconductors

Recent quantum oscillation experiments in underdoped high temperature superconductors seem to imply two paradoxes. The first paradox concerns the apparent non-existence of the signature of the electron pockets in angle resolved photoemission spectroscopy (ARPES). The second paradox is a clear signature of a small electron pocket in quantum oscillation experiments, but no evidence as yet of the corresponding hole pockets of approximately double the frequency of the electron pocket. This hole pockets should be present if the Fermi surface reconstruction is due to a commensurate density wave, assuming that Luttinger sum rule relating the area of the pockets and the total number of charge carriers holds. Here we provide possible resolutions of these apparent paradoxes from the commensurate $d$-density wave theory. To address the first paradox we have computed the ARPES spectral function subject to correlated disorder, natural to a class of experiments relevant to the materials studied in quantum oscillations. The intensity of the spectral function is significantly reduced for the electron pockets for an intermediate range of disorder correlation length, and typically less than half the hole pocket is visible, mimicking Fermi arcs. Next we show from an exact transfer matrix calculation of the Shubnikov-de Haas oscillation that the usual disorder affects the electron pocket more significantly than the hole pocket. However, when, in addition, the scattering from vortices in the mixed state is included, it wipes out the frequency corresponding to the hole pocket. Thus, if we are correct, it will be necessary to do measurements at higher magnetic fields and even higher quality samples to recover the hole pocket frequency.Comment: Accepted version, Phys. Rev. B, brief clarifying comments and updated reference

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance $\sigma_\mathrm{xy}$ and the longitudinal conductance $\sigma_\mathrm{xx}$ are computed. We demonstrate that bond disorder can produce a plateau-like feature centered at $\nu=0$, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between $\pm E_{c}$, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be $2.47\pm 0.04$. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between $\sim 1.0$ and $\sim 7/3$.Comment: 4 pages, 5 figure

Multiferroic coupling in nanoscale BiFeO3

Using the results of x-ray and neutron diffraction experiments, we show that the ferroelectric polarization, in ~22 nm particles of BiFeO3, exhibits a jump by ~30% around the magnetic transition point T_N (~635 K) and a suppression by ~7% under 5T magnetic field at room temperature (<<T_N). These results confirm presence of strong multiferroic coupling even in nanoscale BiFeO3 and thus could prove to be quite useful for applications based on nanosized devices of BiFeO3.Comment: 4 pages including 4 figures and supplementary data; accepted for publication in Appl. Phys. Let

The challenge of weather prediction: What makes it difficult? 3. Old and new ways of weather prediction

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The challenge of weather prediction 1. The basic driving

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A homomorphism theorem and a Trotter product formula for quantum stochastic flows with unbounded coefficients

We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5