Finite Mean Free Path Research Articles

Electrical transport properties of liquid Pb-Li alloys

It is generally observed that electrical transport properties of simple liquid metal based alloys can be explained well in terms of Faber-Ziman theory, 2kF scattering model and finite mean free path approach. However, these approaches give poor description for materials, which show departure from nearly free electron (NFE) model. Taking Pb-Li as a test case of a system showing departure from NFE (which also exhibit compound formation tendency and disparate mass system), a new technique is proposed to compute electrical transport properties using model potential formalism coupled with t-matrix formulation. We have treated valence number of Pb & Li as a parameter in determining phase shifts. Further, rather than calculating phase shift in terms of Muffin-Tin potential, we have used model potential formalism. Present results suggest that compared to other three theoretical approaches mentioned above, present coupling scheme reproduce qualitative features of electrical transport properties of liquid Pb-Li alloys, which can be used further to study electrical transport properties of similar systems.

Incoherent transport in a classical spin liquid

We study the energy and spin transport of the classical spin liquid hosted by the pyrochlore Heisenberg antiferromagnet in the large $S$ limit. Molecular dynamics calculation suggests that both the energy and spin diffusion constants approach finite limits as the temperature tends to zero. We explain our results in terms of an effective disorder model, where the energy/spin-carrying normal modes propagate in a quasi-static disordered spin background. The finite zero temperature limits of the diffusion constants are then naturally understood as a result of the finite mean free path of the normal modes due to the effective disorder.

Phononic transport and simulations of annealing processes in nanometric complex structures

Modeling thermal transport at the nanoscale is a difficult task, especially when external time-varying heating sources and the complexity of the studied systems make computational schemes that rely on accurate particlelike simulations nonaffordable. Alternative strategies based on corrections of the Fourier law could satisfy the trade-off between accuracy and computational efficiency, since they can be implemented in partial differential equation solvers. This continuum approach could also allow for the coupling between thermal transport and other evolving fields related to the generalized temperature field. Here we demonstrate that corrections due to the finite phonon mean free paths can be suitably included in annealing process simulations of three-dimensional nanosystems. Quantitative predictions can be obtained and readily compared with the experimental characterization of the processed samples.

Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a Boltzmann boundary-layer problem to be determined. Matching the inner, boundary layer, solution to the outer, bulk, solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials.

Rare region effects dominate weakly disordered three-dimensional Dirac points

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. We show that even though disorder is perturbatively irrelevant at 3D Dirac points, nonperturbative effects from rare regions give rise to a nonzero density of states and a finite mean free path, with the transport at the Dirac point being dominated by hopping between rare regions. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We also discuss the interplay of disorder with interactions at the Dirac point. Attractive interactions drive a transition into a granular superconductor, with a critical temperature that depends strongly on the disorder distribution. In the presence of Coulomb repulsion and weak retarded attraction, the system can be a Bose glass. Our results apply to all 3D systems with Dirac points, including Weyl semimetals, and overturn a thirty year old consensus regarding the irrelevance of weak disorder at 3D Dirac points.

Instrument response of reflection high energy electron diffraction pole figure

Reflection high-energy electron diffraction (RHEED) pole figure technique using the transmission mode has been developed to study the texture evolution of thin films. For quantitative evaluation of thin film texture, including the dispersion of texture, one would require the knowledge of the instrument response function. We report the characterization of instrument response in RHEED pole figure from an epitaxial CdTe(100) film grown on GaAs(100) substrate. We found the finite mean free path of electrons in a film contributes to the broadening of the poles. In addition, the image processing step size used in the construction of a pole figure also affects the broadening of constructed poles. We apply the measured instrument response in RHEED pole figure to quantitatively analyze a biaxially textured CdTe(111) film deposited on a biaxially textured Ge(111) substrate. Through the deconvolution of the measured dispersions from the poles in the textured CdTe(111) film by the instrument response function, we obtain the out-of-plane and in-plane dispersions of the biaxially textured CdTe(111) film. This method is generic and the instrument response should be considered in order to obtain quantitative texture information for other epitaxial and textured nanostructured films through RHEED pole figure measurements.

The scattering mean free path of cosmic ray particles in isotropic damped plasma wave turbulence

An analytical expression for the mean free path of single-charged cosmic ray particles, especially for positrons, is derived in isotropic plasma wave turbulence, where the crucial scattering of cosmic ray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with oblique magnetosonic waves. In this calculation, viscous damping effects are included, which results in broadening of the resonance function. It is demonstrated that including resonance function broadening ensures a finite mean free path for cosmic ray energies, for which previously reported types of turbulence predicted an infinitely large mean free path.

Finite temperature inelastic mean free path and quasiparticle lifetime in graphene

We adopt the GW approximation and random phase approximation to study finite temperature effects on the inelastic mean free path and quasiparticle lifetime by directly calculating the imaginary part of the finite temperature self-energy induced by electron-electron interaction in extrinsic and intrinsic graphene. In particular, we provide the density-dependent leading order temperature correction to the inelastic scattering rate for both single-layer and double-layer graphene systems. We find that the inelastic mean free path is strongly influenced by finite-temperature effects. We present the similarity and the difference between graphene with linear chiral band dispersion and conventional two dimensional electron systems with parabolic band dispersion. We also compare the calculated finite temperature inelastic scattering length with the elastic scattering length due to Coulomb disorder, and comment on the prospects for quantum interference effects showing up in low density graphene transport. We also carry out inelastic scattering calculation for electron-phonon interaction, which by itself gives rather long carrier mean free paths and lifetimes since the deformation potential coupling is weak in graphene, and therefore electron-phonon interaction contributes significantly to the inelastic scattering only at relatively high temperatures.

Leaky-box approximation to the fractional diffusion model

Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.

Review and limitations of 3D plasma blob modeling with reduced collisional fluid equations

Recent 3D studies on plasma blobs (coherent structures found in the edge region of magnetic confinement devices) have demonstrated that the drift wave instability can strongly limit the blob’s coherency and cross field convective nature that is predicted by 2D theory. However, the dominant unstable drift wave modes that effect plasma blobs were found to exist in parameter regimes that only marginally satisfied several of the major assumptions considered for the validity of the reduced collisional fluid equations used in the study. Namely, the neglect of electron heat flow, finite electron mean free path effects, and thermal ions. A follow up study demonstrated how the drift wave instability might change if a set of equations that does not suffer from the limitations mentioned above were considered. In the present paper, the results of this later work are used to discuss the limitations on using the collisional fluid equations for 3D studies of plasma blobs.

Three-Dimensional Electron Realm inVSe2by Soft-X-Ray Photoelectron Spectroscopy: Origin of Charge-Density Waves

The resolution of angle-resolved photoelectron spectroscopy (ARPES) in three-dimensional (3D) momentum k is fundamentally limited by ill defined surface-perpendicular wave vector k(perpendicular) associated with the finite photoelectron mean free path. Pushing ARPES into the soft-x-ray energy region sharpens the k(perpendicular) definition, allowing accurate electronic structure investigations in 3D materials. We apply soft-x-ray ARPES to explore the 3D electron realm in a paradigm transition metal dichalcogenide VSe2. Essential to break through the dramatic loss of the valence band photoexcitation cross section at soft-x-ray energies is the advanced photon flux performance of our synchrotron instrumentation. By virtue of the sharp 3D momentum definition, the soft-x-ray ARPES experimental band structure and Fermi surface of VSe2 show a textbook clarity. We identify pronounced 3D warping of the Fermi surface and show that its concomitant nesting acts as the precursor for the exotic 3D charge-density waves in VSe2. Our results demonstrate the immense potential of soft-x-ray ARPES to explore details of 3D electronic structure.

COLLISION EFFICIENCY OF BROWNIAN COAGULATION FOR NANOPARTICLES TAKING INTO ACCOUNT THE SLIP BOUNDARY CONDITION ON THE PARTICLE SURFACE

The collision efficiency of Brownian coagulation for monodisperse nanoparticles is considered. A new expression for friction coefficient of particle pair is proposed based on an assumption from a statistical point of view and the relative diffusion coefficient is thus be modified in order to take into account this influence as well as the effects of slip. The modified diffusion coefficient increases the collision efficiency to some extent as expected whether van der Waals interparticle potential is considered or not. A comparison with experimental measurements shows the accuracy of the results predicted by modified theory and the necessity of considering the decrease of friction coefficient due to the random motion of nanoparticles as well as the slip effects arising from the finite mean free path of gas molecules.

THE EFFECT OF ABSORPTION SYSTEMS ON COSMIC REIONIZATION

We use large-scale simulations to investigate the morphology of reionization during the final, overlap phase. Our method uses an efficient three-dimensional smoothing technique that takes into account the finite mean free path due to absorption systems, {lambda}{sub abs}, by only smoothing over scales R{sub s} < {lambda}{sub abs}. The large dynamic range of our calculations is necessary to resolve the neutral patches left at the end of reionization within a representative volume; we find that simulation volumes exceeding several hundred Mpc on a side are necessary in order to properly model reionization when the neutral fraction is {approx_equal} 0.01-0.3. Our results indicate a strong dependence of percolation morphology on a large and uncertain region of model parameter space. The single most important parameter is the mean free path to absorption systems, which serve as opaque barriers to ionizing radiation. If these absorption systems were as abundant as some realistic estimates indicate, the spatial structure of the overlap phase is considerably more complex than previously predicted. In view of the lack of constraints on the mean free path at the highest redshifts, current theories that do not include absorption by Lyman-limit systems, and in particular three-dimensional simulations, may underestimate the abundancemore » of neutral clouds at the end of reionization. This affects predictions for the 21 cm signal associated with reionization, interpretation of absorption features in quasar spectra at z {approx} 5-6, the connection between reionization and the local universe, and constraints on the patchiness and duration of reionization from temperature fluctuations measured in the cosmic microwave background arising from the kinetic Sunyaev-Zel'dovich effect.« less

Importance of Interfaces in Governing Thermal Transport in Composite Materials: Modeling and Experimental Perspectives

Thermal management in polymeric composite materials has become increasingly critical in the air-vehicle industry because of the increasing thermal load in small-scale composite devices extensively used in electronics and aerospace systems. The thermal transport phenomenon in these small-scale heterogeneous systems is essentially controlled by the interface thermal resistance because of the large surface-to-volume ratio. In this review article, several modeling strategies are discussed for different length scales, complemented by our experimental efforts to tailor the thermal transport properties of polymeric composite materials. Progress in the molecular modeling of thermal transport in thermosets is reviewed along with a discussion on the interface thermal resistance between functionalized carbon nanotube and epoxy resin systems. For the thermal transport in fiber-reinforced composites, various micromechanics-based analytical and numerical modeling schemes are reviewed in predicting the transverse thermal conductivity. Numerical schemes used to realize and scale the interface thermal resistance and the finite mean free path of the energy carrier in the mesoscale are discussed in the frame of the lattice Boltzmann-Peierls-Callaway equation. Finally, guided by modeling, complementary experimental efforts are discussed for exfoliated graphite and vertically aligned nanotubes based composites toward improving their effective thermal conductivity by tailoring interface thermal resistance.

The lattice Boltzmann Peierls Callaway equation for mesoscopic thermal transport modeling

The lattice Boltzmann Peierls Callaway (LBPC) method is a recent development of the versatile lattice Boltzmann formalism aimed at a numerical experiment on mesoscale thermal transport in a multiphase phonon gas. Two aspects of mesoscopic thermal transport are discussed: the finite phonon mean free path and the interface thermal resistance. Based on the phonon momentum screening length measured in the LBPC computational apparatus, the validity of the Umklapp collision relaxation time in the Callaway collision operator is examined quantitatively. The discrete nature of the spatio-temporal domain in the LBPC method, along with the linear approximation of the exponential screening mechanism in the Callaway operator, reveals a large discrepancy between the effective phonon mean free path and the analytic phonon mean free path when the relaxation time is small. The link bounce back interface phonon collision rule is used to realize the interface thermal resistance between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for the bulk phonon dynamics, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution uniquely defined by the energy conservation principle. The interface thermal resistance is linearly proportional to the relaxation time of the proposed phonon interface collision rule.

Absence of Casimir regime in two-dimensional nanoribbon phonon conduction

In stark contrast with three-dimensional (3D) nanostructures, we show that boundary scattering in two-dimensional (2D) nanoribbons alone does not lead to a finite phonon mean free path. If combined with an intrinsic scattering mechanism, 2D boundary scattering does reduce the overall mean free path; however, the latter does not scale proportionally to the ribbon width, unlike the well known Casimir regime occurring in 3D nanowires. We show that boundary scattering can be accounted for by a simple Mathiessen-type approach for many different 3D nanowire cross sectional shapes; however, this is not possible in the 2D nanoribbon case, where a complete solution of the Boltzmann transport equation is required. These facts have strong implications for the thermal conductivity of suspended nanostructures.

Site-Specific Stereograph of SiC(0001) Surface by Inverse Matrix Method

The 2π-steradian (full hemisphere) Si 2p and C 1s photoelectron intensity angular distributions (PIADs) of the 6H-SiC(0001) surface 4° off towards the [1\bar100] direction were measured. In a bulk crystal, pairs of mirrored local atomic sites with respect to the 1\bar100 planes exist. Thus, a sixfold symmetry is expected for PIADs from the bulk. However, all the measured PIADs showed a threefold symmetry owing to the preferential appearance of terraces with one type of local atomic site caused by anisotropic step bunching along the [11\bar20] direction. Taking the finite inelastic mean free path of photoelectrons into account, PIADs for one kind of Si and C atomic sites were successfully derived by solving an inverse matrix. Three strong forward focusing peaks due to nearby Si and C atoms have been separated from those formed by farther atoms. They showed a circular dichroism of rotational shift around the incident-light axis, which corresponds to the parallax in stereo viewing.

Superdiffusive and ballistic propagation of protons in solar energetic particle events

AbstractIn this work we show that protons can exhibit both superdiffusive and ballistic propagation, at variance with standard diffusion. We carry out an analysis of impulsive solar energetic particle (SEP) events, for which the observed time profile of energetic particle fluxes represent the propagator of the corresponding transport equation. We show that in the case of superdiffusive or ballistic transport the propagator in the time asymptotic regime has a power law form, and that a fit of the observed time profiles allows to determine the transport regime. Using data obtained from ACE and SoHO spacecraft, two proton and electron events, which exhibit both superdiffusive and ballistic transport, will be shown. The finding of these anomalous regimes implies that no finite mean free path can be defined.

Nonlinear propagation, confinement, and anisotropy of ultrahigh-energy cosmic rays in the Galaxy

We explore the problems of propagation, confinement, and anisotropy of ultrahigh-energy cosmic rays. Previous investigations of plasma-particle interactions are based on a first-order perturbation theory also known as quasilinear theory. It is the subject of this article to employ a nonlinear diffusion theory, namely, the second-order quasilinear theory. We compute the parallel mean free path for slab and for isotropic turbulence for a wave spectrum with small-wave-number cutoff. It is demonstrated that we obtain a finite parallel mean free path even if the Larmor radius of the charged particle is larger than the largest scale of turbulence. Therefore, charged cosmic rays of all energies can be scattered and confined to the Galaxy by the turbulent magnetic fields.

COMPOSITE FERMIONS CLOSE TO THE ONE-HALF FILLING OF THE LOWEST LANDAU LEVEL REVISITED

By strictly adhering to the microscopic theory of composite fermions (CFs) for the Landau-level filling fractions ν e =p/(2p+1), we reproduce, with remarkable accuracy, the surface-acoustic-wave (SAW)-based experimental results by Willett and co-workers concerning two-dimensional electron systems with ν e close to ½. Our results imply that the electron band mass m b , as distinct from the CF mass m⋆, must undergo a substantial increase under the conditions corresponding to ν e ≈ ½. In view of the relatively low aerial electronic densities n e to which the underlying SAW experiments correspond, our finding conforms with the experimental results by Shashkin et al. [Phys. Rev. B 66, 073303 (2002)], concerning two-dimensional electrons in silicon, that signal sharp increase in m b for n e decreasing below approximately 2×1011 cm -2. We further establish that a finite mean-free path ℓ0 is essential for the observed linearity of the longitudinal conductivity σxx(q) as deduced from the SAW velocity shifts.