Single-particle Relaxation Time Research Articles

From Single-Particle to Collective Dynamics in Supercooled Liquids.

It has been recognized recently that the considerable difference between photon correlation (PCS) and dielectric (BDS) susceptibility spectra arises from their respective association with single-particle and collective dynamics. This work presents a model that captures the narrower width and shifted peak position of collective dynamics (BDS), given the single-particle susceptibility derived from PCS studies. Only one adjustable parameter is required to connect the spectra of collective and single-particle dynamics. This constant accounts for cross-correlations between molecular angular velocities and the ratio of the first- and second-rank single-particle relaxation times. The model is tested for three supercooled liquids, glycerol, propylene glycol, and tributyl phosphate, and is shown to provide a good account of the difference between BDS and PCS spectra. Because PCS spectra appear to be rather universal across a range of supercooled liquids, this model provides a first step toward rationalizing the more material-specific dielectric loss profiles.

Nonlinear dielectric relaxation of polar liquids

Molecular dynamics of two water models, SPC/E and TIP3P, at a number of temperatures are used to test the Kivelson-Madden equation connecting single-particle and collective dielectric relaxation times through the Kirkwood factor. The relation is confirmed by simulations and used to estimate the nonlinear effect of the electric field on the dielectric relaxation time. We show that the main effect of the field comes through slowing down of the single-particle rotational dynamics and the relative contribution of the field-induced alteration of the Kirkwood factor is insignificant for water. Theories of nonlinear dielectric relaxation need to mostly account for the effect of the field on rotations of a single dipole in a polar liquid.

Wafer-scale low-disorder 2DEG in 28Si/SiGe without an epitaxial Si cap

We grow 28Si/SiGe heterostructures by reduced-pressure chemical vapor deposition and terminate the stack without an epitaxial Si cap but with an amorphous Si-rich layer obtained by exposing the SiGe barrier to dichlorosilane at 500 °C. As a result, 28Si/SiGe heterostructure field-effect transistors feature a sharp semiconductor/dielectric interface and support a two-dimensional electron gas with enhanced and more uniform transport properties across a 100 mm wafer. At T = 1.7 K, we measure a high mean mobility of (1.8±0.5)×105 cm2/V s and a low mean percolation density of (9±1)×1010 cm−2. From the analysis of Shubnikov–de Haas oscillations at T = 190 mK, we obtain a long mean single particle relaxation time of (8.1±0.5) ps, corresponding to a mean quantum mobility and quantum level broadening of (7.5±0.6)×104 cm2/V s and (40±3) μeV, respectively, and a small mean Dingle ratio of (2.3±0.2), indicating reduced scattering from long range impurities and a low-disorder environment for hosting high-performance spin-qubits.

The scattering time of electrons in a GaAs/InGaAs/GaAs quantum well including temperature and exchange-correlation effects

The ratio of the scattering and single-particle relaxation time of a quasi-two-dimensional electron gas (Q2DEG) in a finite lattice-mismatched GaAs/InGaAs/GaAs quantum well was investigate at zero and finite temperatures, taking into account the exchange-correlation effects via a local-field correction with three approximations for the LFC, G = 0, GH, and GGA. We studied the dependence of the surface roughness, roughness-induced piezoelectric, remote and homogenous background charged impurity scattering on the carrier density and quantum well width. In the case of zero temperature and Hubbard local-field correction our results reduced to those of different theoretical calculations. At low density, the exchange-correlation effects depend strongly on the ratio τt/τs. While at high density many-body effects due to exchange and correlation considerably modified the ratio of the scattering and single-particle relaxation time. We found that, for densities and temperatures considered T = 0,3TF in this study, the temperature affected weakly on the time ratio for four scatterings. Furthermore, with the change of quantum well width, the effect of LFC and temperatures act on the ratio τt/τs are negligible for the roughness-induced piezoelectric and remote charged impurity scattering, and are notable for the surface roughness and homogenous background charged impurity scattering.

Single-particle relaxation time in doped semiconductors beyond the Born approximation

We compare the magnitudes of the single-particle relaxation time exactly computed in the variable phase approach with those computed in the first Born approximation for doped semiconductors such as Si and GaAs, assuming that the Coulomb impurities are randomly distributed centers. We find that for typical dopant concentrations in Si, the Born approximation can overestimate the single-particle relaxation time by roughly 40% and underestimate it by roughly 30%. Finally, we show that the strong interference of phase shifts is missing in the strong scattering regime where the Born approximation fails.

Effect of random vacancies on the electronic properties of graphene and T graphene: a theoretical approach

In this communication we present together four distinct techniques for the study of electronic structure of solids : the tight-binding linear muffin-tin orbitals (TB-LMTO), the real space and augmented space recursions and the modified exchange-correlation. Using this we investigate the effect of random vacancies on the electronic properties of the carbon hexagonal allotrope, graphene, and the non-hexagonal allotrope, planar T graphene. We have inserted random vacancies at different concentrations, to simulate disorder in pristine graphene and planar T graphene sheets. The resulting disorder, both on-site (diagonal disorder) as well as in the hopping integrals (off-diagonal disorder), introduces sharp peaks in the vicinity of the Dirac point built up from localized states for both hexagonal and non-hexagonal structures. These peaks become resonances with increasing vacancy concentration. We find that in presence of vacancies, graphene-like linear dispersion appears in planar T graphene and the cross points form a loop in the first Brillouin zone similar to buckled T graphene that originates from $\pi$ and $\pi$* bands without regular hexagonal symmetry. We also calculate the single-particle relaxation time, $\tau(\vec{q})$ of $\vec{q}$ labeled quantum electronic states which originates from scattering due to presence of vacancies, causing quantum level broadening.

Relaxation times and charge conductivity of silicene

We investigate the transport and single particle relaxation times of silicene in the presence of neutral and charged impurities. The static charge conductivity is studied using the semiclassical Boltzmann formalism when the spin-orbit interaction is taken into account. The screening is modeled within Thomas-Fermi and random phase approximations. We show that the transport relaxation time is always longer than the single particle one. Easy electrical controllability of both carrier density and band gap in this buckled two-dimensional structure makes it a suitable candidate for several electronic and optoelectronic applications. In particular, we observe that the dc charge conductivity could be easily controlled through an external electric field, a very promising feature for applications as electrical switches and transistors. Our findings would be qualitatively valid for other buckled honeycomb lattices of the same family, such as germanine and stanine.

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. II. RPA response functions and collective modes

The spin and density response functions in the random phase approximation (RPA) are derived by linearizing the kinetic equation including a magnetic field, the spin-orbit coupling, and mean fields with respect to an external electric field. Different polarization functions appear describing various precession motions showing Rabi satellites due to an effective Zeeman field. The latter turns out to consist of the mean-field magnetization, the magnetic field, and the spin-orbit vector. The collective modes for charged and neutral systems are derived and a threefold splitting of the spin waves dependent on the polarization and spin-orbit coupling is shown. The dielectric function including spin-orbit coupling, polarization and magnetic fields is presented analytically for long wave lengths and in the static limit. The dynamical screening length as well as the long-wavelength dielectric function shows an instability in charge modes, which are interpreted as spin segregation and domain formation. The spin response describes a crossover from damped oscillatory behavior to exponentially damped behavior dependent on the polarization and collision frequency. The magnetic field causes ellipsoidal trajectories of the spin response to an external electric field and the spin-orbit coupling causes a rotation of the spin axes. The spin-dephasing times are extracted and discussed in dependence on the polarization, magnetic field, spin-orbit coupling and single-particle relaxation times.

Carrier screening, transport, and relaxation in three-dimensional Dirac semimetals

A theory is developed for the density and temperature-dependent carrier conductivity in doped three-dimensional (3D) Dirac materials focusing on resistive scattering from screened Coulomb disorder due to random charged impurities (e.g., dopant ions and unintentional background impurities). The theory applies both in the undoped intrinsic (``high-temperature,'' $T\ensuremath{\gg}{T}_{F})$ and the doped extrinsic (``low-temperature,'' $T\ensuremath{\ll}{T}_{F})$ limit with analytical scaling properties for the carrier conductivity obtained in both regimes, where ${T}_{F}$ is the Fermi temperature corresponding to the doped free carrier density (electrons or holes). The scaling properties describing how the conductivity depends on the density and temperature can be used to establish the Dirac nature of 3D systems through transport measurements. We also consider the temperature-dependent conductivity limited by the acoustic phonon scattering in 3D Dirac materials. In addition, we theoretically calculate and compare the single-particle relaxation time ${\ensuremath{\tau}}_{s}$, defining the quantum level broadening, and the transport scattering time ${\ensuremath{\tau}}_{t}$, defining the conductivity, in the presence of screened charged impurity scattering. A critical quantitative analysis of the ${\ensuremath{\tau}}_{t}/{\ensuremath{\tau}}_{s}$ results for 3D Dirac materials in the presence of long-range screened Coulomb disorder is provided.

Interaction effects on dynamic correlations in noncondensed Bose gases

We consider dynamic, i.e., frequency-dependent, correlations in non-condensed ultracold atomic Bose gases. In particular, we consider the single-particle correlation function and its power spectrum. We compute this power spectrum for a one-component Bose gas, and show how it depends on the interatomic interactions that lead to a finite single-particle relaxation time. As another example, we consider the power spectrum of spin-current fluctuations for a two-component Bose gas and show how it is determined by the spin-transport relaxation time.

Transport properties of the two-dimensional electron gas in AlP quantum wells at finite temperature including magnetic field and exchange–correlation effects

We investigate the transport scattering time, the single-particle relaxation time and the magnetoresistance of a quasi-two-dimensional electron gas in a GaP/AlP/GaP quantum well at zero and finite temperatures. We consider the interface-roughness and impurity scattering, and study the dependence of the mobility, scattering time and magnetoresistance on the carrier density, temperature and local-field correction. In the case of zero temperature and Hubbard local-field correction our results reduce to those of Gold and Marty (Physica E 40 (2008) 2028; Phys. Rev. B 76 (2007) 165309). We also discuss the possibility of a metal–insulator transition which might happen at low density.

Electronic transport in two-dimensional Si:Pδ-doped layers

We investigate theoretically two-dimensional (2D) electronic transport in Si:P $\ensuremath{\delta}$-doped layers limited by charged-dopant scattering. Since the carrier density is approximately equal to the dopant impurity density, the density dependent transport shows qualitatively different behavior from that of the well studied 2D Si MOSFETs (metal-oxide-semiconductor field-effect transistors) where the carrier density is independent of the impurity density. We find that the density dependent mobility of the Si:P system shows nonmonotonic behavior which is exactly opposite of the nonmonotonicity observed in Si MOSFETs---in the Si:P system the mobility first decreases with increasing density and then it increases slowly with increasing density above a typical density ${10}^{14}$ cm${}^{\ensuremath{-}2}$ (in contrast to Si MOSFETs where the mobility typically increases with density first and then slowly decreases at high density as surface roughness scattering dominates). In the low-density limit (or strong screening limit) mobility decreases inversely with increasing density, but in the high-density limit (or weak-screening limit) it slowly increases due to the finite width effects of the 2D layer. In the intermediate density regime ($1/a<2{k}_{F}<{q}_{TF}$, where $a$, ${k}_{F}$, and ${q}_{TF}$ are the confinement width of the $\ensuremath{\delta}$ layer, Fermi wave vector, and Thomas-Fermi screening wave vector, respectively) the density dependent mobility is approximately a constant at the minimum value. However, the calculated mean free path increase monotonically with density. We also compare the transport scattering time relevant to the mobility and the single-particle relaxation time relevant to the quantum level broadening, finding that the transport scattering time could be much larger than the single-particle scattering time unlike in Si MOSFETs where they are approximately equal.

Electron and hole scattering in short-period InGaAs/InP superlattices

The combination of photoluminescence and magneto-transport measurements is used to study the single-particle relaxation time and the transport scattering time in short-period InGaAs/InP superlattices. Both the single-particle relaxation times of the electrons and of the holes were obtained in the same samples and were shown to be determined by the remote-impurity scattering. The transport scattering time for electrons was found to be dominated by the interface-roughness scattering with lateral length Λ=10 nm and height Δ = 0.13 nm. We also discuss the importance of multiple-scattering effects for small well widths and of alloy scattering for large well widths.

Transport scattering time and single-particle relaxation time in ZnO/MgZnO heterostructures: Many-body effects

Recent experimental results regarding the transport properties of ZnO/MgZnO heterostructures with very high mobility (μ≤1.8×105cm2/Vs) are analyzed. In the electron density range of the experiment, the two-dimensional electron gas in ZnO/MgZnO heterostructures is strongly correlated with a large Wigner-Seitz parameter 4 < rs < 12. We demonstrate that many-body effects (exchange and correlation), described by a local-field correction, are very large in this density range. They reduce the screening properties of the two-dimensional electron gas and strongly reduce the transport scattering time and the single-particle relaxation time at low electron densities. For such samples, we also discuss the peak mobility, the metal-insulator transition, and the magnetoresistance in a parallel magnetic field.

Single-particle relaxation time of the two-dimensional electron gas in Si/SiGe: Many-body effects

The single-particle relaxation time of the two-dimensional electron gas in SiGe/Si/SiGe quantum wells is calculated. Many-body effects beyond the random-phase approximation become important at low electron density. For charged impurity scattering (remote doped), the importance of these many-body effects as functions of the electron density and spacer width is analyzed. Induced by many-body effects, a strong reduction of the single-particle relaxation time at low electron densities is predicted. The relation with the transport scattering time is described, multiple-scattering effects are commented, and the determination of many-body effects in existing samples is discussed.

Ordered phases of itinerant Dzyaloshinsky-Moriya magnets and their electronic properties

A field theory appropriate for magnets that display helical order due to the Dzyaloshinsky-Moriya mechanism, a class that includes MnSi and FeGe, is used to derive the phase diagram in a mean-field approximation. The helical phase, the conical phase in an external magnetic field, and recent proposals for the structure of the A-phase and the non-Fermi-liquid region in the paramagnetic phase are discussed. It is shown that the orientation of the helical pitch vector along an external magnetic field within the conical phase occurs via two distinct phase transitions. The Goldstone modes that result from the long-range order in the various phases are determined, and their consequences for electronic properties, in particular the specific heat, the single-particle relaxation time, and the electrical and thermal conductivities, are derived. Various aspects of the ferromagnetic limit, and qualitative differences between the transport properties of helimagnets and ferromagnets, are also discussed.

Mobility and metal–insulator transition of the two-dimensional electron gas in SiGe/Si/SiGe quantum wells

We consider the mobility of the interacting two-dimensional electron gas as realized in SiGe/Si/SiGe quantum wells. For zero temperature we calculate the mobility as function of the electron density for remote charged-impurity scattering and we take into account exchange-correlation effects and multiple-scattering effects. Multiple-scattering effects give rise to a metal–insulator transition at low electron density. Our calculation is in good agreement with experimental results obtained with remote doped SiGe/Si/SiGe quantum wells having electron densities near the metal–insulator transition. We discuss the critical density of the metal–insulator transition as function of the remote doping distance and make some predictions. The single-particle relaxation time and spin-polarization effects are also considered.

Anomalous diffusion, structural relaxation and shear thinning in glassy hard spherefluids

The stochastic nonlinear Langevin equation theory of the single-particle dynamics ofglassy hard sphere fluids and suspensions has been applied to address severalissues raised by recent experimental and simulation studies. The theoreticallypredicted degree of non-Fickian behaviour at intermediate times, and the slowstructural relaxation component of the small wavevector incoherent dynamic structurefactor, are compared quantitatively with recent measurements and reveal goodagreement. A roughly power law growth, with a common exponent, of the classic andalternative non-Gaussian parameter amplitudes with mean alpha relaxation timeis predicted, and qualitative similarities with a multi-point susceptibility thatquantifies dynamic heterogeneity effects are noted. The nonlinear rheology version ofthe theory has been quantitatively applied to explain recent measurements ofshear-induced acceleration of the single-particle relaxation time on the local cage scale.The resulting no adjustable parameter calculations are in remarkable agreementwith the experimental observations for the absolute magnitude, volume fractiondependence and fractional power law scaling aspects of the shear thinning phenomenon.

Single-particle relaxation time versus transport scattering time in a two-dimensional graphene layer

We theoretically calculate and compare the single particle relaxation time $({\ensuremath{\tau}}_{s})$ defining the quantum level broadening and the transport scattering time $({\ensuremath{\tau}}_{t})$ defining the Drude conductivity in two-dimensional (2D) graphene layers in the presence of screened charged impurity scattering and short-range defect scattering. We find that the ratio ${\ensuremath{\tau}}_{t}∕{\ensuremath{\tau}}_{s}$ strongly increases with increasing ${k}_{F}{z}_{i}$ and $\ensuremath{\kappa}$, where ${k}_{F}$, ${z}_{i}$, and $\ensuremath{\kappa}$ are, respectively, the Fermi wave vector, the separation of the substrate charged impurities from the graphene layer, and the background lattice dielectric constant. A critical quantitative comparison of the ${\ensuremath{\tau}}_{t}∕{\ensuremath{\tau}}_{s}$ results for graphene with those for the corresponding modulation-doped semiconductor structures is provided, showing significant differences between these two 2D carrier systems.

Mobility of thin AlAs quantum wells: Theory compared to experiment

For interface-roughness scattering and for zero temperatures, we compare theoretical results for the transport properties of the electron gas present in thin AlAs quantum wells with experimental results for a well of width L=45Å. The importance of a density dependent effective mass is discussed. For the mobility, reasonable agreement between theory and experiment is obtained by taking into account multiple scattering effects, which lead to a metal-insulator transition. We predict the single-particle relaxation time. With a density dependent effective mass, the calculated critical electron density of the metal-insulator transition is found to be in good agreement with the experimental value.