Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Magnetotransport measurements have been performed on Fibonacci lateral superlattices (FLSLs) -- two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence, LSLLSLS..., with L/S=tau (the golden ratio). Complicated commensurability oscillation (CO) is observed, which can be accounted for as a superposition of a series of COs each arising from a sinusoidal modulation representing the characteristic length scale of one of the self-similar generations in the Fibonacci sequence. Individual CO components can be separated out from the magnetoresistance trace by performing a numerical Fourier band-pass filter. From the analysis of the amplitude of a single-component CO thus extracted, the magnitude of the corresponding Fourier component in the potential modulation can be evaluated. By examining all the Fourier contents observed in the magnetoresistance trace, the profile of the modulated potential seen by the electrons can be reconstructed with some remaining ambiguity about the interrelation of the phase between different components.Comment: 11 pages, 10 figures, added references in Introduction, minor revision

Effect of Oscillating Landau Bandwidth on the Integer Quantum Hall Effect in a Unidirectional Lateral Superlattice

We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.Comment: 7 pages, 6 figures, minor revisio

Transport of polymer particles in a oil-water flow in porous media: enhancing oil recovery

We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.Comment: 20 pages, 9 Figures Submitted to Transport in Porous Medi

Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level

We have observed marked transport anisotropy in short period (a=92 nm) unidirectional lateral superlattices around filling factors nu=5/2 and 7/2: magnetoresistance shows a sharp peak for current along the modulation grating while a dip appears for current across the grating. By altering the ratio a/l (with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron density n_e, it is shown that the nu=5/2 anisotropic features appear in the range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its height/depth up to 250 mK. Tilt experiments reveal that the structures are slightly enhanced by an in-plane magnetic field B_| perpendicular to the grating but are almost completely destroyed by B_| parallel to the grating. The observations suggest the stabilization of a unidirectional charge-density-wave or stripe phase by weak external periodic modulation at the second Landau level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and reference

Modulation Induced Phase Transition from Fractional Quantum Hall to Stripe State at nu=5/3

We have investigated the effect of unidirectional periodic potential modulation on the fractional quantum Hall (FQH) state at filling factors nu=5/3 and 4/3. For large enough modulation amplitude, we find that the resistivity minimum at nu=5/3 gives way to a peak that grows with decreasing temperature. Density matrix renormalization group calculation reveals that phase transition from FQH state to unidirectional striped state having a period sim 4 l (with l the magnetic length) takes place at nu=1/3 (equivalent to nu=5/3 by the particle-hole symmetry) with the increase of the modulation amplitude, suggesting that the observed peak is the manifestation of the stripe phase.Comment: 4 pages, 6 figures; minor revisio

Origin of positive magnetoresistance in small-amplitude unidirectional lateral superlattices

We report quantitative analysis of positive magnetoresistance (PMR) for unidirectional-lateral-superlattice samples with relatively small periods (a=92-184 nm) and modulation amplitudes (V_0=0.015-0.25 meV). By comparing observed PMR's with ones calculated using experimentally obtained mobilities, quantum mobilities, and V_0's, it is shown that contribution from streaming orbits (SO) accounts for only small fraction of the total PMR. For small V_0, the limiting magnetic field B_e of SO can be identified as an inflection point of the magnetoresistance trace. The major part of PMR is ascribed to drift velocity arising from incompleted cyclotron orbits obstructed by scatterings.Comment: 12 pages, 9 figures, REVTe

Commutators, Lefschetz fibrations and the signatures of surface bundles

We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature. From these we derive new upper bounds for the minimal genus of a surface representing a given element in the second homology of a mapping class group.Comment: 20 pages, 7 figures, accepted for publication in Topolog

Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal ($\sigma_{xx}$) and off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$ with $\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between $\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.Comment: 21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matte