Generalized Drude Model Research Articles

Iteration of semiconductor Bloch equations for ultrashort laser pulse propagation

The numerical propagation of intense laser pulses through bulk material requires the recurrent calculation of the nonlinear material response. To describe the optical Kerr effect and the current in the conduction band for macroscopic propagation distances, very simplified models are typically used. Recent studies of the response of dielectrics to intense few-cycle pulses have revealed that ionization does not accumulate monotonically, but conduction bands are populated both irreversibly and reversibly during a laser cycle. The reversible (or transient or virtual) population of the conduction bands is not captured by simple response models. Here, an efficient iteration based on the semiconductor Bloch equations for three bands is developed, which consistently captures the laser cycle resolved interband polarization and intraband current. The full calculation of the nonlinear material response at each propagation step is avoided, instead only the incremental modification of the previous propagation step is calculated. The iteration is particularly well-suited for very short pulses and can be applied for intensities above the critical value at which perturbation theory does not converge. Furthermore, it is shown that virtual currents and dynamic Bloch oscillations are mechanisms which are missing in the Drude model, but these two mechanisms prevail for short intense pulses. Therefore, a generalized Drude model is derived from the SBEs, which is capable to account for arbitrary band shapes and both real and virtual ionization.

Heavily n-doped Ge: Low-temperature magnetoresistance properties on the metallic side of the metal–nonmetal transition

We report here an experimental and theoretical study on the magnetoresistance properties of heavily phosphorous doped germanium on the metallic side of the metal–nonmetal transition. An anomalous regime, formed by negative values of the magnetoresistance, was observed by performing low-temperature measurements and explained within the generalized Drude model, due to the many-body effects. It reveals a key mechanism behind the magnetoresistance properties at low temperatures and, therefore, constitutes a path to its manipulation in such materials of great interest in fundamental physics and technological applications.

Generalized Drude model and electromagnetic screening in metals and superconductors**Project supported by the National Natural Science Foundation of China (Grant No. 11504164).

Electromagnetic screening is studied from the perspective of fluid mechanics by generalizing the Drude theory, which unifies three known results: Thomas–Fermi screening of the longitudinal field in both metals and superconductors, the skin effect of the transverse field in metals, and the Meissner effect in superconductors. In the special case of superfluid electrons, we slightly generalize the London equations to incorporate the longitudinal electric fields. Moreover, regarding the experiments, our study points out that the dynamical measurement may overestimate the superfluid density.

Infrared properties of cuprates in the pseudogap state: a study of Mitrović-Fiorucci and Sharapov-Carbotte scattering rates

The frequency dependent scattering rate of generalized Drude model contains important information on the electronic structure and on scattering mechanism. In the present investigation, we study the frequency dependent scattering rate of cuprates (Mitrović-Fiorucci/Sharapov-Carbotte scattering rate) in the pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ) density of states. First, with the energy dependent density of states, the scattering rate shows a depression at low energy coming from the opening of the pseudogap. Second, the evolution of 1/τ(ω,T) with temperature shows the observed increase in scattering rate with temperature at lower frequencies and the temperature independence of 1 /τ(ω) at higher frequencies. Third, the signature of the thresholds due to the boson density of states and to the electronic density of states are also observed. These signatures are qualitatively in accord with the experiments.

Optical conductivity of the R-Cd quasicrystals and approximants

Recently, a new family of R-Cd binary icosahedral quasicrystals has been discovered [1]. Using optical reflectance spectroscopy, we have examined the quasicrystal GdCd7.98and the approximants GdCd6and YCd6. To explain the unique behaviour of electrons in a quasiperiodic lattice Mayou [2] created a model of electron transport due to anomalous diffusion of wave packets scattering from the quasiperiodic lattice. We have determined the optical conductivity of the above-mentioned materials from 7.5 meV to 5.5 eV and have used Mayou's model of optical conductivity for approximants and quasicrystals, σ1∝ Re[ (1/(γ-iω))^(2β-1) ], to describe the low frequency behaviour. Despite the concern of Mayou of not being able to differentiate experimentally between normal metallic conductivity of ballistic electrons, β=1, and sub-ballistic conductivity, 1/2<β<1, we clearly see β≍3/4 in the intraband peak of the icosahedral approximants, which has not been observed before. Before this work, the only unambiguously Drude-like peak seen in any quasicrystal or their approximant occurred in the decagonal approximant γ-brass, which was fit with exactly β=1 [3]. However, unlike the approximants in our study, this sample of γ-brass was admittedly not a good approximant to a quasicrystal with its small lattice constant. In the GdCd7.98quasicrystal, we observe low frequency behaviour that lacks a Drude peak but is not nearly perfectly linear as seen by others. In this case, the low frequency behaviour is qualitatively similar to the diffusive regime, 0<β<1/2, that is often seen. However, it is not adequately modelled by Mayou's generalized Drude model. With these results, unlike in previous optical conductivity studies, we have a striking difference in the low frequency conductivity that suggests that there is a difference in the physics of the optical conductivity of periodic and quasiperiodic lattices that needs to be explored.

Linear optical and electronic properties of the polar metallic ruthenate (Sr,Ca)Ru2O6

Using first-principles calculations, we compute the linear optical properties for cation ordered (Sr,Ca)Ru2O6. Our calculations show that this polar ferromagnetic metallic oxide exhibits optical anisotropy along the principal directions of the optical indicatrix owing to the absence of inversion symmetry in the crystal structure. The calculated reflectivity is used to locate the onset of the inter-band transitions at an energy of 1.3 eV. Comparing the optical conductivity with the electronic band structure, we identify the possible optical transitions. Finally, we apply the generalized Drude model to deduce an enhancement of the effective mass, m* ∼ 4.9me, in ordered (Sr,Ca)Ru2O6. Moreover, we show that removal of the polar distortions decrease the effective mass to m* ∼ 4.4me, suggesting that control over the amplitude of the polar displacements could be used to tune the degree of electronic correlation in oxide conductors without inversion symmetry.

Microwave conductivity of sorted CNT assemblies.

Recent progress with tailored growth and post-process sorting enables carbon nanotube (CNT) assemblies with predominantly metallic or semi-conducting concentrations. Cryogenic and microwave measurements performed here show transport dimensionality and overall order increasing with increasing metallic concentration, even in atmospheric doping conditions. By 120 GHz, the conductivity of predominantly semi-conducting assemblies grew to 400% its DC value at an increasing growth rate, while other concentrations a growth rate that tapered off. A generalized Drude model fits to the different frequency dependent behaviors and yields useful quality control parameters such as plasma frequency, mean free path, and degree of localization. As one of the first demonstrations of waveguides fabricated from this material, sorted CNTs from both as-made and post-process sources were inserted into sections of practical micro-strip. With both sources, sorted CNT micro-strip increasingly outperformed the unsorted with increasing frequency-- illustrating that sorted CNT assemblies will be important for high frequency applications.

A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation

Unveiling the full potential of doped silicon for electronic, photonic, and plasmonic application at THz frequencies requires a thorough understanding of its high-frequency transport properties. In this letter, we present a comprehensive numerical characterization of the frequency-dependent (0–2.5 THz) complex conductivity of silicon at room temperature over a wide range of doping densities (1014−1018 cm−3). The conductivity was calculated using a multiphysics computational technique that self-consistently couples ensemble Monte Carlo (EMC) simulation of carrier transport, the finite-difference time-domain (FDTD) solution to Maxwell's equations, and molecular dynamics (MD) for the treatment of short-range Coulomb interactions. Our EMC/FDTD/MD numerical results complement the experimental data that only exist for a select few doping densities. Moreover, we show that the computed complex conductivity of Si at THz frequencies can be accurately described by a generalized Drude (GD) model with doping-dependent parameters that capture the cross-over from phonon-dominated to Coulomb-dominated electron transport as the doping density increases. The simplicity of the GD model enables one to readily compute the complex conductivity of silicon for any doping density within the range studied here.

Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry

We have developed a terahertz time-domain magneto-optical ellipsometry to deduce the effective mass, scattering time, density, and type (n or p) of free carriers independently. The parameters are derived from diagonal and off-diagonal components of the complex dielectric tensor obtained by measurements of magneto-optical Kerr effects under a magnetic field of 0.46 T using the generalized Drude model. The derivation of these parameters for n-type InAs wafers with different carrier densities is demonstrated. The carrier density dependence of the effective mass agrees well with previously reported experimental results and theoretical calculations that take into account nonparabolicity of conduction bands.

Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy

Far-infrared absorption and refractive index of a ZnO wafer were measured as a function of temperature below 120 K using terahertz (THz) time domain spectroscopy. The accompanying frequency-dependent complex conductivity gives an accurate picture of electron dynamics because the measured range of 0.2--2.5 THz brackets the scattering rate. The frequency-dependent conductivity shows the general trends predicted by the Drude model but with significant deviations that are better fit by the generalized Drude model, which allows for a distribution of carrier relaxation times. Conductivity increases with increasing temperature as electrons are thermally activated from shallow donor states, with calculated donor energy of 27 meV and density of $1.4\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }{\text{cm}}^{\ensuremath{-}3}$. Mobilities of $\ensuremath{\sim}2000\text{ }{\text{cm}}^{2}\text{ }{\text{V}}^{\ensuremath{-}1}\text{ }{\text{s}}^{\ensuremath{-}1}$ are measured and do not vary significantly with temperature over 60--120 K.

Infrared spectroscopy of the interface charge in a ZnO field-effect transistor

We used far-infrared transmission spectroscopy to probe the electrostatically induced charge carriers in a ZnO field-effect transistor. The carrier absorption spectrum exhibits a non-Drude, incoherent conduction behavior at low gate-source voltages (VGS<40V), which evolves toward a standard Drude behavior as VGS is increased. This change is explained successfully by a generalized Drude model. We find that the interface carriers undergo strong backscattering collisions during the channel conduction and the microscopic scattering angle changes with VGS.

Temperature- and frequency-dependent optical properties of ultrathin Au films

While the optical properties of thin metal films are well understood in the visible and near-infrared range, little has been done in the midinfrared and far-infrared region. Here we investigate ultrathin gold films prepared on $\text{Si}(111)(7\ifmmode\times\else\texttimes\fi{}7)$ in UHV by measuring in the frequency range between 500 and $7000\text{ }{\text{cm}}^{\ensuremath{-}1}$ and for temperatures between 300 and 5 K. The nominal thickness of the gold layers ranges between one monolayer and 9 nm. The frequency and temperature dependences of the thicker films can be well described by the Drude model of a metal when taking into account classical size effects due to surface scattering. The films below the percolation threshold exhibit a nonmetallic behavior; the reflection increases with frequency and decreases with temperature. The frequency dependence can partly be described by a generalized Drude model. The temperature dependence does not follow a simple activation process. For monolayers we observe a transition between surface states around $1100\text{ }{\text{cm}}^{\ensuremath{-}1}$.

Optical evidence for the proximity to a spin-density-wave metallic state in $\mathsf{Na_{0.7}CoO_2}$

We present the optical properties of \na single crystals, measured over a broad spectral range as a function of temperature ($T$). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate ($\Gamma$) and effective mass ($m^*$) of the itinerant charge carriers. We find that $\Gamma(\omega)\sim \omega$ at low temperatures and for $\omega > T$. This suggests that \na is at the verge of a spin-density-wave metallic phase.

Optical Study of Two-Dimensional Organic Metal (EO-TTP) 2AsF 6 (EO-TTP=2-(4,5-Ethylenedioxy-1,3-Dithiol-2-Ylidene)-5-(1,3-Dithiol-2-Ylidene)-1,3,4,6-Tetrathiapentalene)

Polarized reflectance spectra were measured on the conductive (010) plane of metallic (EO-TTP) 2AsF 6 single crystal. At room temperature, well-defined plasma edges appeared in both directions parallel ( E|| a) and perpendicular ( E⊥ a) to the molecular stack. The intra- and inter-stack transfer integrals were estimated from the plasma frequencies in the framework of tight-binding model. Based on these transfer integrals, we suggested that the Fermi surface was open in the k c direction. Using a generalized Drude model, we obtained the frequency dependence of relaxation rate, which conformed to γ(ω)=γ 0+bω 2 in the frequency range 1800–5500 cm −1.

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB 2 (T c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 ≤ ω < 100000 cm -1 . The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/τ (ω) and the mass renormalization ratio m * (ω)/m = 1 +λ(ω) exhibit clear frequency dependence. The electron-phonon coupling strength is estimated to be λ ∼ 1.5 ± 0.5 while the plasma frequency ω p is 2.4 eV.

Generalized Drude model: unification of ballistic anddiffusive electron transport

For electron transport in parallel-plane semiconducting structures, a model isdeveloped that unifies ballistic and diffusive transport and thus generalizesthe Drude model. The unified model is valid for arbitrary magnitude of themean free path and arbitrary shape of the conduction band edge profile.Universal formulas are obtained for the current-voltage characteristic in thenondegenerate case and for the zero-bias conductance in the degenerate case,which describe in a transparent manner the interplay of ballistic and diffusivetransport. The semiclassical approach is adopted, but quantum correctionsallowing for tunnelling are included. Examples are considered, in particularthe case of chains of grains in polycrystalline or microcrystallinesemiconductors with grain size comparable to, or smaller than, the mean freepath. Substantial deviations of the results of the unified model from those ofthe ballistic thermionic-emission model and of the drift-diffusion model arefound. The formulation of the model is one-dimensional, but it is argued thatits results should not differ substantially from those of a fullythree-dimensional treatment.

The mid-infrared dielectric function of NBCO in the a-b planefrom 85 K to 300 K

Results are reported on the a-b plane dielectric function(ε) of thin-film c-axis NdBa2Cu3O7-δ withclose to optimal oxygen doping (Tc~90 K) in the mid-infrared(wavelength 3.392 µm) over the temperature range 85 K to300 K. An attenuated total reflectance technique based on theexcitation of surface plasmon polaritons is used. The results show that|εr| decreases quasi-linearly with increasing temperature,while εi is invariant with temperature to within experimentaluncertainties. Representative values are ε = [εr + iεi] = (-12.9±0.6) + i(23.0±1.5) at T~295 Kand ε = (-15.7±0.7) + i(23.5±1.1) at T~90 K.The raw data are interpreted in terms of the generalized Drude model whichgives effective scattering rates (1/τ*) that increase withtemperature from about 3800 cm-1 at 90 K to about 4300 cm-1 at 295 K. There are indications of a superlinear T-dependencein the scattering, 1/τ*; a fit to a function of the form 1/τ* = A + BTα gives α = 2.8±0.7. The effectiveplasma frequency, ωp*, with an average value ofapproximately 21 000 cm-1 was independent of temperature.

Optical Properties of Laser‐Produced Plasmas

AbstractThe interaction of high intensity femtosecond laser pulses with matter allows the production of plasmas with high electron densities. This enables the study of basic plasma physics in regimes relevant to astrophysics, atomic physics, or in strongly correlated plasmas. Much of the understanding of such plasmas depends on the knowledge of the optical properties. The diagnostic requires theoretical models for the interpretation of experimental data. We study the dielectric function and the electric conductivity in the framework of a generalized Drude model. The required collision frequencies are taken in Born and strong coupling (T‐matrix) approximations. Furthermore, we try to give an estimation of the influence of nonlinear, high frequency effects of the electrical field. In order to describe the temporal evolution of the plasma, we determine the composition of the plasma solving Saha's equation. Therefore we investigate different approximations for the effective ionization energy including Padé formulas for the correlation part of the chemical potential.

Infrared absorptances of partially ordered alloys at elevated temperatures

The infrared absorptances of highly polished Ti-6Al-4V and 304 stainless steel have been measured between 2 and 20 μm and at temperatures up to 550 °C. Small positive temperature coefficients for both alloys were observed. A generalized Drude model has been developed to interpret the data; the weak temperature dependence of the absorptance has been attributed to the relatively small effect of phonon scattering in these disordered alloys.