Extended Drude Model Research Articles

Theoretical study on time response of semiconductor photorefractive effects under subpicosecond ultra-fast X-rays.

A theoretical model that can efficiently calculate the refractive index response of semiconductors under ultrafast X-ray radiation is established based on the photorefractive effect of semiconductors. The proposed model is used to interpret X-ray diagnostics experiments, and the results are in good agreement with experiments. In the proposed model, a rate equation model of free carrier density calculation is adopted with the X-ray absorption cross-sections calculated by atomic codes. The two-temperature model is used to describe the electron-lattice equilibration and the extended Drude model is applied to calculate the transient refractive index change. It is found that faster time response can be achieved for semiconductors with shorter carrier lifetime and sub-picosecond resolution can be obtained for InP and [Formula: see text]. The material response time is not sensitive to X-ray energy and the diagnostics can be used in the 1-10 keV energy range. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Terahertz complex conductivity of stretchable semitransparent composite films made from polymeric materials PDMS and PEDOT:PSS

We investigate the terahertz complex conductivity spectra of stretchable composite films with semitransparency for visible light that are fabricated by blending the conducting polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) with the elastomer poly(dimethylsiloxane) (PDMS) in various weight ratios. We find that the PDMS-based composite exhibits a conductivity whose real part increases to 0.77 S/cm at 1.0 THz with increasing PEDOT:PSS blending ratio while it has a stretchability of more than ∼130%. A fitting analysis of the complex conductivity spectra with an extended Drude model shows that carriers in the PDMS-based composite become denser linearly and also less localized gradually as the blending ratio is increased.

Terahertz complex conductivity of cellulose nanocrystal based composite films controlled with PEDOT:PSS blending ratio

We investigate the terahertz complex conductivity spectra of cellulose nanocrystal (CNC) based composite films fabricated with different blending ratios of the conducting polymer poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) and without/with glycerol additive. A partially localized nature of carriers in the composite is clearly seen in the obtained spectral shapes of complex conductivity and is well described by an extended Drude model. We find that the carriers become denser and less localized with increasing PEDOT:PSS blending ratio and that the addition of glycerol to the composite is efficacious in enhancing carrier delocalization as well as mechanical flexibility.

Erratum: Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity [Phys. Rev. Applied 11, 064062 (2019)

Erratum: Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity [Phys. Rev. Applied 11, 064062 (2019)

Extended Drude Model Analysis of the Optical Spectra of Correlated Electron Systems in a d-Wave Superconducting State

Correlation information in strongly correlated electron systems can be obtained using an extended Drude model. An interesting method related to the extended Drude model analysis of superconducting optical data was proposed recently, and it has attracted attention from researchers. This method aims to extract the optical self-energy of quasiparticles (or residual unpaired electrons) from measured optical data in the superconducting state. However, this residual optical self-energy is a partial optical self-energy. The interpretation and significance of this partial optical self-energy is unclear. We investigate this method using a reverse process with simple electron-boson spectral density functions. With our obtained results, we conclude that the residual (or partial) optical self-energy is difficult to interpret because it contains unphysical features, in particular, a negative optical effective mass. The present study clarifies the extended Drude analysis method for superconducting optical data.

Casimir force, causality, and the Gurzhi model

An extended Drude model, termed as the Gurzhi model, which takes into account the electron-phonon and electron-electron interactions, is applied to calculate the Casimir force between two metallic plates. It is shown that although the dielectric permittivity of the Gurzhi model has a first order pole in the upper half-plane of complex frequencies and, thus, violates the causality principle, it can be used in a restricted frequency interval in combination with the experimental permittivity determined by the optical data for the complex index of refraction. The imaginary part of the Gurzhi dielectric permittivity of Au at low frequencies demonstrates better agreement with the permittivity given by the optical data than the simple Drude model. The Casimir pressure between two Au plates is computed using the Gurzhi, Drude and plasma model approaches, taking into account the optical data, as well as with the simple Drude and plasma models. The contribution of the electron-electron scattering to the Casimir pressure is estimated. Although a comparison with the measurement data of two precise experiments show that the Gurzhi model does not resolve the Casimir puzzle, the obtained results suggest further clarification of this fundamental problem.

Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity

Optical nonlinearity due to intraband transitions (which is important for the application of epsilon-near-zero nonlinearity in metasurfaces and active plasmonics) requires a model to fully predict the spectrum, for design considerations. The extended Drude model, presented here, serves this purpose. It further elucidates the origin of the nonlinearity to be due to both band nonparabolicity and temperature-dependent mobility. The model matches experiment well for the representative compound indium tin oxide, and simplifies the description of spectrally resolved optical nonlinearities of transparent conductive oxides.

Terahertz complex conductivity of nanofibrillar cellulose-PEDOT:PSS composite films

We investigate the terahertz transmission through flexible composite films that contain nanofibrillar cellulose (NFC) and different blending percentages of the conductive polymer poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS). The real part of terahertz complex conductivity is found to decrease with decreasing frequency for each NFC composite film and to approach a finite positive value dependent on the PEDOT:PSS blending percentage in the limit of zero frequency. Both the real and imaginary parts of complex conductivity spectra can be fitted simultaneously with an extended Drude model that describes a partially localized nature of carriers. Our spectral analysis indicates that carriers in the NFC composite become denser and also less localized as the PEDOT:PSS blending percentage is increased.

Rotation effect on spin current in curved space-time

The spin-orbit interaction and spin Hall effect have drawn special attention. Not only theoretical predictions have been made, but also the generation of spin currents has been achieved in experiment. In this paper, we study the spin current and the spin Hall conductivity under the influence of rotation in the curved space-time. Our work shows that the nontrivial geometries could modify the spin-orbital interaction. By using the extended Drude model, we calculate the spin-dependent force and obtain a correction to this force by non-mediocre geometry. When considering the rotation effect, the general Dirac equation is given. The Hamiltonian under the non-relativistic approximation is obtained by the Foldy-Wouthuysen transform. According to this, we calculate the spin current and spin Hall conductance. The polarization vector is deformed due to the effect of the rotation in the curved space-time. The magnitude and direction of the spin current are changed because of the correction to rotation, and the spin Hall conductivity. The nontrivial space-time geometry leads to the anisotropic nature of the spin current. Our work uses a general method that does not depend on the model, so the result can be used to analyze the electromagnetic dynamics of charged spin particles in quantum Hall systems, and it also helps to theoretically study the defects in crystals. Our results can also be extended to the optical subsystem. Considering the spin effect of photons, based on the spin-orbit coupling of photon, a light splitting phenomenon emerges in an inhomogeneous medium, which is the spin hall effect of photon. Our discussion has a certain reference value for studying the behavior of the photonic spin Hall effect in the static gravitational field. At the same time, using the optical chips to simulate curved space-time, photon manipulation and precision measurement can give some theoretical support.

Low-energy interband transition effects on extended Drude model analysis of optical data of correlated electron system

Low-energy interband transition effects on extended Drude model analysis of optical data of correlated electron system

Analysis of optical data using extended Drude model and generalized Allen’s formulas

Extended Drude model formalism has been successfully utilized for analyzing optical spectra of strongly correlated electron systems including heavy-fermion systems and high-Tc superconducting iron pnictides and cuprates. Furthermore, generalized Allen’s formulas have been developed and applied to extract the electron-boson spectral density function from measured optical data of high temperature superconductors including cuprates in various material phases. Here we used a reverse process to obtain various optical quantities starting from two typical electron-boson spectral density model functions for three intriguing (normal, pseudogap, and d-wave superconducting) material phases in cuprates. We also assigned the calculated optical results to designated regions in the phase diagram of hole-doped cuprates and compared them with the corresponding measured optical spectra of Bi2Sr2CaCu2 (Bi-2212). This comparison suggested that this way of optical data analysis can be a convincing method to study correlated electrons in the copper oxide superconductors and other superconducting systems as well.

Influences of the coordinate dependent noncommutative space on charged and spin currents

We study the charged and spin currents on a coordinate dependent noncommutative space. Starting from the noncommutative extended relativistic equation of motion, the nonrelativistic approximation is obtained by using the Foldy–Wouthuysen transformation, and then the charged and spin currents are derived by using the extended Drude model. We find that the charged current is twisted by modifying the off-diagonal elements of the Hall conductivity, however, the spin current is not affected up to leading order of the noncommutative parameter.

An Alternative Approach to the Extended Drude Model

The original Drude model, proposed over a hundred years ago, is still used today for the analysis of optical properties of solids. Within this model, both the plasma frequency and quasiparticle scattering rate are constant, which makes the model rather inflexible. In order to circumvent this problem, the so-called extended Drude model was proposed, which allowed for the frequency dependence of both the quasiparticle scattering rate and the effective mass. In this work we will explore an alternative approach to the extended Drude model. Here, one also assumes that the quasiparticle scattering rate is frequency dependent; however, instead of the effective mass, the plasma frequency becomes frequency-dependent. This alternative model is applied to the high Tc superconductor Bi2Sr2CaCu2O8+δ (Bi2212) with Tc = 92 K, and the results are compared and contrasted with the ones obtained from the conventional extended Drude model. The results point to several advantages of this alternative approach to the extended Drude model.

Terahertz spectroscopic evidence of non-Fermi-liquid-like behavior in structurally modulated PrNiO3 thin films

The intertwined and competing energy scales of various interactions in rare-earth nickelates $R\mathrm{Ni}{\mathrm{O}}_{3}$ ($R=\mathrm{La}$ to Lu) hold potential for a wide range of exotic ground states realized upon structural modulation. Using terahertz (THz) spectroscopy, the low-energy dynamics of a novel non-Fermi liquid (NFL) metallic phase induced in compressive $\mathrm{PrNi}{\mathrm{O}}_{3}$ thin film was studied by evaluating the quasiparticle scattering rate in the light of two distinct models over a wide temperature range. First, evaluating THz conductivity in the framework of extended Drude model, the frequency-dependent scattering rate is found to deviate from the Landau Fermi liquid (LFL) behavior, thus, suggesting NFL-like phase at THz frequencies. Second, fitting THz conductivity to the multiband Drude-Lorentz model reveals the band-dependent scattering rates and provides microscopic interpretation of the carriers contributing to the Drude modes. This is first evidence of NFL-like behavior in nickelates at THz frequencies consistent with dc conductivity, which also suggests that THz technology is indispensable in understanding emerging electronic phases and associated phenomena. We further demonstrate that the metal-insulator transition in nickelates has the potential to design efficient THz modulators.

Revisiting optical properties of MgB2 with a high-quality sample prepared by a HPCVD method

We investigated a high-quality MgB2 thin film with a thickness of ~1000 nm on an Al2O3 substrate using optical spectroscopy. We measured the reflectance spectra of the film at various temperatures both below, and above, the superconducting transition temperature, Tc simeq 40 K. An earlier study showed that when the sample surface is exposed to air the optical properties of the surface change immediately, however, the saturated change is negligibly small in the far-infrared region. The optical conductivity spectrum in the normal state shows two (narrow and broad) Drude modes, with the narrow Drude mode being dominant in the low frequency region below 1000 cm−1. Our study, which uses a good-quality sample, provides more reliable data on the optical properties of MgB2, in a similar spectral range. The optical data is analyzed further using an extended Drude model, and the electron-phonon spectral density function, α2F(ω), is extracted. The spectral density function α2F(ω) features two peaks: a small one near 114 cm−1, and a strong peak around the 550 cm−1 where the B-B bond stretching phonon exists. Our data in the superconducting state does not show the expected energy shift of the onset of scattering associated with the α2F(ω) peaks.

Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics

Excitation of surface plasmons in silver nanoparticles is a promising method for enhancing light trapping. The present paper reports results for the optical properties of the nanocrystalline silver thin films in attempt to understand the effects of the particle size. The microstructure of the films was probed by scanning electron-microscopy, Atomic Force microscopy (AFM) and X-ray diffraction (XRD). The size of the crystallites/grains calculated from the XRD measurements by the Debye-Scherrer formula is in a good agreement with the AFM results. The optical properties were determined from spectral ellipsometric measurements. It was shown that the Drude-Lorentz model is suitable for characterization of porous films, while an island structure required the extended Drude model with frequency dependent damping parameter, Γ. It was demonstrated that the maximum of the imaginary part of the complex permittivity,ε^ω=ε′ω+iε′′ω, that is due to the transverse oscillations of the polarization of the silver grains, can be positioned in the energy range of 1.5–2.8eV in dependence of the deposition rate; it's been shifted to higher energies when reducing the grains size. Contemporary, the resulting changes in the surface/volume ratio lead to shifts the maximum in the loss function Im−1ε^ω from 3.8 to 3.5eV.

Infrared Spectroscopic Evidences of Strong Electronic Correlations in (Sr1-xLax)3Ir2O7.

We report on infrared spectroscopic studies of the electronic response of the (Sr1−xLax)3Ir2O7 system. Our experiments revealed hallmarks of strong electronic correlations in the evolution of the electronic response across the filling-controlled insulator-metal transition. We observed a collapse of the Jeff = 1/2 Mott gap accompanying the transfer of the spectral weight from the high-energy region to the gap region with electron doping. The intraband conductivity at the metallic side of the transition was found to consist of coherent Drude-like and incoherent responses. The sum rule and the extended Drude model analyses further indicated a large mass enhancement. Our results demonstrate a critical role of the electronic correlations in the charge dynamics of the (Sr1−xLax)3Ir2O7 system.

Intrinsic carrier scattering mechanism in anataseTiO2investigated by ultraviolet-pump terahertz-probe spectroscopy

We measured the optical conductivity $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}(\ensuremath{\omega})$ spectra caused by photocarriers in anatase $\mathrm{Ti}{\mathrm{O}}_{2}$ by applying ultraviolet-pump terahertz-probe spectroscopy on epitaxially grown thin films. Drude model analyses of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}(\ensuremath{\omega})$ spectra reveal that, in the terahertz region, the reduced mass ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{m}$) of the carriers is greater and their damping constant ($\ensuremath{\gamma}$) is smaller than those in the infrared region. With regard to the extended Drude model, these differences can be attributed to the frequency dependence of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{m}$ and $\ensuremath{\gamma}$ originating from carrier-phonon scatterings. Furthermore, the interaction between carriers and Ti-O stretching modes in the $500--1000\ensuremath{-}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ region strongly influences the intrinsic carrier scattering mechanism in anatase $\mathrm{Ti}{\mathrm{O}}_{2}$.

Anomalous behavior of coupling constant near the magnetic phase transition of Ni-doped Ba-122 pnictides

We investigated Ni-doped Ba-122 pnictide single crystals at two different doping levels (BaFe2−xNixAs2; x = 0.05 (underdoped) and 0.10 (optimally doped)) using optical spectroscopy. We analyze measured optical data with an extended Drude model and a generalized Allen’s formalism. We extracted the electron-boson spectral density function using an approximate single-band approach from measured optical scattering rate. We observed that an anomalous behavior in the coupling constant obtained from the electron-boson spectral density function takes place near the magnetic transition temperature of the underdoped sample. This anomaly has not been observed in cuprate system. Nevertheless, overall temperature and doping dependent properties of the electron-boson spectral density of pnictides are similar to those of cuprates. This may indicate that these two different high-temperature superconducting systems share a same mechanism for their superconductivity.

Femtosecond laser sintering of copper nanoparticles

The ultrafast melting of copper nanoparticles (NPs) induced by a femtosecond laser pulse with duration of 100 fs and wavelength of 800 nm is investigated theoretically and experimentally. The Cu pattern fabricated from sintering of a Cu NP-dispersed film by the femtosecond laser at a repetition rate of 80 MHz is experimentally studied. A one-dimensional two-temperature model with temperature-dependent material properties, including the extended Drude model for dynamic optical properties and the thermophysical properties, is employed to simulate the particles ultrafast melting and re-solidification process.