Dimensional Hole Research Articles

Betti number signatures of homogeneous Poisson point processes

The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: beta{0} is the number of connected components and beta{k} effectively counts the number of k-dimensional holes. Although they are appealing natural descriptors of shape, the higher-order Betti numbers are more difficult to compute than other measures and so have not previously been studied per se in the context of stochastic geometry or statistical physics. As a mathematically tractable model, we consider the expected Betti numbers per unit volume of Poisson-centered spheres with radius alpha. We present results from simulations and derive analytic expressions for the low intensity, small radius limits of Betti numbers in one, two, and three dimensions. The algorithms and analysis depend on alpha shapes, a construction from computational geometry that deserves to be more widely known in the physics community.

A microscopic model for the black hole: Black string phase transition

Computations in general relativity have revealed an interesting phase diagram for the black hole–black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by ‘boosting’ plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of ( 4 + 1 )-dimensional near-extremal holes and ( 3 + 1 )-dimensional near-extremal holes respectively (the latter is a uniform black string in 4 + 1 dimensions). We propose a simple model that interpolates between these limits and reproduces most of the features of the phase diagram. These results should help us understand how ‘fractionation’ of branes works in general situations.

Wire-mesh honeycomb catalysts for selective catalytic reduction of NO with NH3

Both flat and corrugated wire mesh sheets were coated with aluminum powder by using electrophoretic deposition (EPD) method. Controlled thermal sintering of coated samples yielded uniform porous aluminum layer with a thickness of 100 μm that was attached firmly on the wire meshes. Subsequent controlled calcination formed a finite thickness of Al2O3 layer on the outer surface of each deposited aluminum particles, which resulted in the formation of Al2O3/Al double-layered composite particles that were attached firmly on the wire surface to form a certain thickness of porous layer. A rectangular-shaped wire-mesh honeycomb (WMH) module with triangular-shaped channels was manufactured by packing alternately the flat sheet and corrugated sheet of the Al2O3/Al-coated wire meshes. This WMH was further coated with V2O5-MoO3-WO3 catalyst by wash-coating method to be applied for the selective catalytic reduction (SCR) of NO with NH3. With an optimized catalyst loading of 16 wt%, WMH catalyst module shows more than 90% NO conversion at 240 °C and almost complete NO conversion at temperatures higher than 300 °C at GHSV 5,000 h−1. When compared with conventional ceramic honeycomb catalyst, WMH catalyst gives NO conversion higher by 20% due to reduced mass transfer resistance by the existence of three dimensional opening holes in WMH.

Extra dimensions at the CERN LHC via mini-black holes: Effective Kerr-Newman brane-world effects

We solve Einstein equations on the brane to derive the exact form of the brane-world-corrected perturbations in Kerr-Newman singularities, using Randall-Sundrum and Arkani-Hamed-Dimopoulos-Dvali (ADD) models. It is a consequence of such models that Kerr-Newman mini-black holes can be produced in LHC. We use this approach to derive a normalized correction for the Schwarzschild Myers-Perry radius of a static $(4+n)$-dimensional mini-black hole, using more realistic approaches arising from Kerr-Newman mini-black hole analysis. Besides, we prove that there are four Kerr-Newman black hole horizons in the brane-world scenario we use, although only the outer horizon is relevant in the physical measurable processes. Parton cross sections in LHC and Hawking temperature are also investigated as functions of Planck mass (in the LHC range 1--10 TeV), mini-black hole mass, and the number of large extra dimensions in brane-world large extra-dimensional scenarios. In this case a more realistic brane-effect-corrected formalism can achieve more precisely the effective extra-dimensional Planck mass and the number of large extra dimensions---in the Arkani-Hamed-Dimopoulos-Dvali model---or the size of the warped extra dimension---in Randall-Sundrum formalism.

Spin-Hall effect in two-dimensional mesoscopic hole systems

The spin Hall effect in two dimensional hole systems is studied by using the four-terminal Landauer-B\"{u}ttiker formula with the help of Green functions. The spin Hall effect exists even when there are {\em not} any correlations between the spin-up and -down heavy holes (light holes) and when the $\Gamma$-point degeneracy of the heavy hole and light hole bands is lifted by the confinement or recovered by the strain. When only a heavy hole charge current without any spin polarization is injected through one lead, under right choice of lead voltages, one can get a pure heavy (light) hole spin current, combined with a possible impure light (heavy) hole spin current from another two leads. The spin Hall coefficients of both heavy and light holes depend on the Fermi energy, devise size and the disorder strength. It is also shown that the spin Hall effect of two dimensional hole systems is much more robust than that of electron systems with the Rashba spin-orbit coupling and the spin Hall coefficients do not decrease with the system size but tend to some nonzero values when the disorder strength is smaller than some critical value.

Formation of a Freely Suspended Membrane via a Combination of Interfacial Reaction and Wetting

Applying poly(ethoxysiloxane) (a liquid non-water-soluble polymer that can be hydrolyzed and cross-linked by diluted acids) to an air/pH 1 water interface gave rise to thin homogeneous solid layers. These layers were strong enough to be transferable to electron microscopy grids with holes of dimensions up to 150 microm and covered the holes as freely suspended membranes. No homogeneous layers were formed at an air/pH 5 water interface. Brewster angle microscopy images show that the poly(ethoxysiloxane) is not spontaneously forming a wetting layer on water. It initially forms lenses, which slowly spread out within several hours. We conclude that the spreading occurs simultaneously with the hydrolysis and cross-linking of the poly(ethoxysiloxane) and that the reaction products finally assist the complete wetting of the water surface.

Intrinsic Spin Hall Effect in the Two-Dimensional Hole Gas

We show that two types of spin-orbit coupling in the 2 dimensional hole gas, with and without inversion symmetry breaking, contribute to the intrinsic spin-Hall effect. Furthermore, the vertex correction due to impurity scattering vanishes in both cases, in sharp contrast to the case of usual Rashba coupling in the electron band. Recently, the spin-Hall effect in a hole doped GaAs semiconductor has been observed experimentally by Wunderlich et al. [ Phys. Rev. Lett. 94, 047204 (2005).]. From the fact that the lifetime broadening is smaller than the spin splitting, and the fact impurity vertex corrections vanish in this system, we argue that the observed spin-Hall effect should be in the intrinsic regime.

Influence of geometrical and electrical parameters of masking layers on the electrochemical etching of silicon for single trench formation

Deep single trenches can be produced at the edge of apertures of protective films masking the surface of silicon samples. This macropore formation, from polarized HF based solutions, is electrically activated depending on the mask geometrical and physical parameters whatever the silicon type or the electrolyte composition. The mask thickness increase is known to induce deeper trenches. In this paper, we show that we can predict and localize this phenomenon by simulating two dimensional hole current distributions below the mask. We demonstrate also the influence of the material permittivity on trench depth. These 2D simulation results are correlated with experimental results.

BREAKDOWN OF THE QUANTUM HALL EFFECTS IN HOLE SYSTEMS AT HIGH INDUCED CURRENTS

The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly-sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρxx takes a very low value. The sweep rate and temperature dependence of these induced currents are in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ1/3, and the spin split energy gap, g*μ B B.

Electron hole liquid in silicon single quantum wells

We have carried out photoluminescence measurements on the two dimensional electron hole liquid in perfectly crystalline Si quantum wells with SiO 2 barriers. The condensation of excitons in an EHL is strongly enhanced in 2D geometry. Formation of liquid nanodroplets with size varying with laser power is seen. Carriers are submitted to a quantum confinement regime for sufficiently small thickness. We present a model taking into account 2D many-body effects and the increase of the Coulomb interaction due to the dielectric mismatch between the Si well and the dielectric barrier. Results are in good agreement with photoluminescence measurements.

A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes

No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d>=5, where the system of equations can be reduced to "a master equation" - a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.

Superconductivity of YBa 2Cu 3O 7− δ type crystal by 2D electron–hole system

An origin of superconductivity in YBa 2Cu 3O 7− δ is discussed by considering the two dimensional electron and hole systems. In particular, the mechanism to have two peaks where δ takes the two value of 1/10 and 1/6 is discussed.

The covering spectrum of a compact length space

We define a new spectrum for compact length spaces and Riemannian manifolds called the “covering spectrum” which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ>0 which identify the distinct δ covers of the space. We investigate the relationship between this covering spectrum, the length spectrum, the marked length spectrum and the Laplace spectrum. We analyze the behavior of the covering spectrum under Gromov–Hausdorff convergence and study its gap phenomenon.

Transport of the quasi-three-dimensional hole gas in a magnetic field in the ultra-quantum limit

We observed anomalous oscillations in the magnetoresistance of quasi-three dimensional holes in a magnetic field in the ultra-quantum limit. For this study we used wide p-type AlGaAs parabolic quantum wells in the presence of the in-plane magnetic field. We attribute the anomalous oscillations to the formation of the correlated electronic states.

Self-Consistent Subband Structure and Mobility of Two Dimensional Holes in Strained SiGe MOSFETs

The motivation to research strained SiGe layers on relaxed silicon is to enhance the very low hole mobility observed in conventional Si MOSFETs. This is mainly due to large hole effective masses and strong surface roughness scattering. In this work, the buried SiGe quantum well, chosen as the active channel for carrier transport, enhances mobility in two ways. First, the carriers are confined in the SiGe well and are removed from the Si-SiO2 interface, so interface roughness is not a big factor. Secondly, strained SiGe has a lower hole effective mass than unstrained Si and the mobility is expected to increase as the Ge concentration increases. We present the results of a self-consistent subband structure and low field mobility calculations for holes in a Si-SiGe heterostructure FET. Our results are in agreement with the experimental work by Garone and coworkers, indicating the validity of our model.

Fabrication of GaAs hole array as a 2D-photonic crystal and their application to photonic bandgap waveguide

A two dimensional (2D) GaAs hole array with a high aspect ratio was successfully fabricated by dry etching techniques using a highly ordered alumina membrane as a mask. The reflection spectra of the GaAs hole array shows characteristics of the photonic bandgap (PBG) calculated by using the 2D triangular lattice structure. Various defect lines were formed etching in the GaAs hole array using focused ion beam. The defect-type PBG waveguide was experimentally demonstrated.

Scaling behavior of metal–insulator transitions in a Si/SiGe two dimensional hole gas

We report the temperature dependence of magnetotransport measurements in a Si/SiGe two-dimensional hole gas (2DHG) and we analyze the curves in terms of scaling. A reentrant insulating transition is observed at filling factor ν=1.5, followed by a second high field insulating phase at ν<1. A scaling behavior in temperature of the width of the longitudinal conductivity, its second derivative and the slope of the Hall conductivity has been observed, for both the transitions to the insulating state.

Confinement symmetry, mobility anisotropy, and metallic behavior in(311)AGaAs two-dimensional holes

We study two dimensional hole systems confined to GaAs quantum wells grown on the (311)A surface of GaAs substrates. Such samples exhibit an in-plane mobility anisotropy. At constant 2D hole density, we vary the symmetry of the quantum well potential and measure the temperature dependence of the resistivity along two different current directions, in a regime where the samples exhibit metallic behavior. The symmetry has a significant and non-trivial effect on the metallic behavior. Moreover, differences between the temperature-dependence of the resistivity along the two mobility directions point to specific scattering mechanisms being important in the expression of the metallic behavior.

Phase diagram of the integer quantum Hall effect inp-type germanium

We experimentally study the phase diagram of the integer quantized Hall effect, as a function of density and magnetic field. We used a two dimensional hole system confined in a Ge/SiGe quantum well, where all energy levels are resolved, because the Zeeman splitting is comparable to the cyclotron energy. At low fields and close to the quantum Hall liquid-to-insulator transition, we observe the floating up of the lowest energy level, but NO FLOATING of any higher levels, rather a merging of these levels into the insulating state. For a given filling factor, only direct transitions between the insulating phase and higher quantum Hall liquids are observed as a function of density. Finally, we observe a peak in the critical resistivity around filling factor one.

Two dimensional phonon-drag thermopower in Si 0.87Ge 0.13/Si (001) heterostructure grown by MBE

Results of thermoelectric power measurements are presented for two dimensional hole gas (2DHG) formed at the normal interface of modulation boron doped Si/Si 0.87Ge 0.13/(001) Si fully strained heterostructure for the first time in the temperature range 1.5 to 25 K. The modulation-doped 2DHG sample has carrier sheet density p s of 2×10 11 cm −2 and its mobility value μ is 1.11×10 4 cm 2 V −1 s −1 at liquid 4He temperature. The thermoelectric power is found to be dominated by the phonon drag contribution. A fit to phonon-drag thermopower theory yields a value of 5.5 eV for the screened acoustic phonon deformation potential. A Kohn anomaly is observed at ∼3.5±0.5 K.