Drude Component Research Articles

Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7

The discovery of superconductivity with a critical temperature of about 80 K in La3Ni2O7 single crystals under pressure has received enormous attention. La3Ni2O7 is not superconducting under ambient pressure but exhibits a transition at T ∗ ≃ 115 K. Understanding the electronic correlations and charge dynamics is an important step towards the origin of superconductivity and other instabilities. Here, our optical study shows that La3Ni2O7 features strong electronic correlations which significantly reduce the electron’s kinetic energy and place this system in the proximity of the Mott phase. The low-frequency optical conductivity reveals two Drude components arising from multiple bands at the Fermi level. The transition at T ∗ removes the Drude component exhibiting non-Fermi liquid behavior, whereas the one with Fermi-liquid behavior is barely affected. These observations in combination with theoretical results suggest that the Fermi surface dominated by the Ni-d3z2−r2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{3{z}^{2}-{r}^{2}}$$\\end{document} orbital is removed due to the transition at T ∗. Our experimental results provide pivotal information for understanding the transition at T ∗ and superconductivity in La3Ni2O7.

Observation of Electronic Structure Modification in the Hidden Order Phase of CeCoSi

CeCoSi with no local inversion symmetric crystal structure (P4/nmm) exhibits a phase transition of unknown origin (Hidden Order: HO) at about 12 K (T0) above the antiferromagnetic transition temperature (TN = 9.4 K). The electronic structure change across T0 was investigated with high-precision optical reflection spectroscopy. The optical spectrum changed from a typical metallic behavior above T0 to a gap-like structure at around 15 meV below T0. The gap-like structure was unchanged across TN except for the narrowing of the Drude component of carriers due to the suppression of magnetic fluctuations. This result suggests a slight change from the typical metallic electronic structure above T0 to that with an energy gap near the Fermi level in the HO phase. The change in electronic structure in the HO phase was concluded to be due to electron/valence instability.

Analysis of the temperature dependent optical properties of V1−xWxO2 thin films

Vanadium dioxide is one of the most promising materials that can be used to control and tune in real time the optical properties of nanoscale devices due to its ability to perform a Metal-Insulator Transition (MIT). In this paper, we report the optical and structural properties of undoped and W-doped V1-xWxO2 vanadium dioxide thin films deposited on oxidized silicon substrates using magnetron sputtering. The structural properties determined by X-ray diffraction showed not only the transition from a monoclinic to a rutile phase when crossing the metal–insulator transition temperature (TMIT) but also a coexistence of phases for the tungsten-doped VO2 even at room temperature. It is also shown that TMIT decreases from 69.6°C to 41.6°C as x increases from 0 to 3%. A point-by-point fitting method is proposed to reliably extract the refractive index and extinction coefficient from spectroscopic ellipsometry measurements as a function of temperature and tungsten concentration. This approach avoids all the correlations between the thickness and the refractive index well known in absorbent films calling into question the uniqueness of the results. The dielectric function is then calculated from the point by point refractive index. A model based on Tauc-Lorentz oscillators in the insulating phase to which a Drude component is added in the metallic phase provides information on the levels of the energy bands and the plasma frequency of the films. The calculation of reflectance and transmittance of V1-xWxO2 thin films highlights the effect of W doping on thermochromic performance.

Effects of niobium doping on the charge density wave and electronic correlations in the kagome metal Cs(V1−xNbx)3Sb5

The transport and optical properties of the Nb-doped Cs(V$_{1-x}$Nb$_{x}$)$_{3}$Sb$_{5}$ with x = 0.03 and 0.07 have been investigated and compared with those of the undoped CsV$_{3}$Sb$_{5}$. Upon Nb doping, the charge-density wave (CDW) transition temperature $T_{\text{CDW}}$ is suppressed, and the superconducting temperature $T_{c}$ rises. The residual resistivity ratio decreases with Nb doping, suggesting an increase of disorder. For all compounds, the optical conductivity in the pristine phase reveals two Drude components (D1 and D2). The substitution of Nb causes an increase of D1 alongside a reduction of D2 in weight, which implies a change of the Fermi surface. The total Drude weight is reduced with increasing Nb content, signifying an enhancement of electronic correlations. Below $T_{\text{CDW}}$, while the optical conductivity clearly manifests the CDW gap in all materials, the gapped portion of the Fermi surface shrinks as the Nb content grows. A comprehensive analysis indicates that the change of the Fermi surface, the enhancement of electronic correlations, the shrinkage of the removed Fermi surface by the CDW gap, and the increase of disorder may all have a considerable impact on the interplay between the CDW and superconductivity in Cs(V$_{1-x}$Nb$_{x}$)$_{3}$Sb$_{5}$.

Strange metal electrodynamics across the phase diagram of Bi2−xPbxSr2−yLayCuO6+δ cuprates

Unlocking the mystery of the strange metal state has become the focal point of high T$_{c}$ research, not because of its importance for superconductivity, but because it appears to represent a truly novel phase of matter dubbed `quantum supreme matter'. Detected originally through high magnetic field, transport experiments, signatures of this phase have now been uncovered with a variety of probes. Our high resolution optical data of the low T$_{c}$ cuprate superconductor, Bi$_{2-x}$Pb$_{x}$Sr$_{2-y}$La$_{y}$CuO$_{6+\delta}$ allows us to probe this phase over a large energy and temperature window. We demonstrate that the optical signatures of the strange metal phase persist throughout the phase diagram. The strange metal signatures in the optical conductivity are two-fold, (i): a low energy Drude response with Drude width on the order of temperature and (ii): a high energy conformal tail with doping dependent power-law exponent. While the Drude weight evolves monotonously throughout the entire doping range studied, the spectral weight contained in the high energy conformal tail appears to be doping and temperature independent. Our analysis further shows that the temperature dependence of the optical conductivity is completely determined by the Drude parameters. Our results indicate that there is no critical doping level inside the superconducting dome where the carrier density starts to change drastically and that the previously observed 'return to normalcy' is a consequence of the increasing importance of the Drude component relative to the conformal tail with doping. Importantly, both the doping and temperature dependence of the resistivity are largely determined by the Drude width.

Photon-modulated linear and nonlinear anomalous Hall effects in type-II semi-Dirac semimetals

Two-dimensional semi-Dirac materials, with quadratic dispersion in one direction and linear dispersion in the orthogonal direction, provide a route to formation of the Chern-insulating states in solids. Within the framework of the Floquet theory, we investigate the photon-modulated linear and nonlinear anomalous Hall effect (AHE) in type-II semi-Dirac semimetals and find that rich topological phases, as well as interesting phenomena related to the topological transitions, can be realized and manipulated by circularly polarized light (CPL). By tuning the CPL parameters, we can control the local inverted gaps independently and switch the system between different topological phases optionally. We also demonstrate that, when the Fermi level locates outside the gap, the Drude component of the conductivity can contribute to the AHE as well, because of the anisotropy of the electronic structure. Besides, the nonlinear Hall effect due to the Berry curvature dipole can be observable when the inversion symmetry between opposite valleys is broken. Our findings are helpful to understand the topological properties of the emergent type-II semi-Dirac semimetals.

Evolution of the electronic structure of Ru-doped single-crystal iridates Sr2Ir1−xRuxO4

We investigated Ru-doped single-crystal $5d$ iridates, ${\mathrm{Sr}}_{2}{\mathrm{Ir}}_{1\ensuremath{-}x}{\mathrm{Ru}}_{x}{\mathrm{O}}_{4}$, at three different doping concentrations ($x=0.01$, 0.07, and 0.10) using optical spectroscopy. The undoped pristine compound (${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$) is known as a novel ${J}_{\text{eff}}=1/2$ Mott insulator. Remarkably, the optical conductivity spectra of all three samples exhibited insulating behavior, although we observed weak Drude components in the optical conductivity spectra down to the lowest temperature of 30 K. The charge-carrier densities of the Ru-doped iridates estimated from the Drude components are significantly smaller than the expected values estimated from the nominal Ru-doping concentrations. Herein, we provide the temperature- and doping-dependent electronic structure evolution of Ru-doped iridates. We expect that our results will be useful for understanding the intriguing Ru-doping-dependent properties of $5d$ iridate ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$.

Optical properties of the antiferromagnetic Heusler alloy Ru2CrGe

The results of optical measurements in the long wavelength infra-red (IR) range on the antiferromagnetic Heusler alloy Ru2CrGe with a Néel temperature of 13 K are reported. At 9 K there is absence of a Drude component in the absorption coefficient indicating the insulating nature of Ru2CrGe at this temperature. The absorption coefficient was observed to increase steeply around 50–70 cm−1 at all temperatures measured in this study.

Evolution of charge dynamics in FeSe1−xTex : Effects of electronic correlations and nematicity

We systematically studied in-plane optical conductivity of $\mathrm{Fe}{\mathrm{Se}}_{1\ensuremath{-}x}{\mathrm{Te}}_{x}$ thin films fabricated on $\mathrm{Ca}{\mathrm{F}}_{2}$ substrates for $x=0$, 0.1, 0.2, and 0.4. This system shows a large enhancement of superconducting transition temperature ${T}_{\mathrm{c}}$ at $x\ensuremath{\approx}0.2$ and a gentle decrease in ${T}_{\mathrm{c}}$ with further increasing $x$. The low-energy optical conductivity spectrum is described by the sum of narrow and broad Drude components, associated with coherent and incoherent charge dynamics, respectively. With increasing Te content, the spectral weight of the narrow Drude component decreases, whereas the total weight of the two Drude components increases. As a consequence, the fraction of the narrow Drude weight significantly decreases, indicating that Te substitution leads to stronger electronic correlations. Below the nematic transition temperature, the narrow Drude weight decreases with decreasing temperature. This indicates the reduction of the coherent carrier density, resulting from the Fermi-surface modification induced by the development of the orbital order. The reduction of the narrow Drude weight with temperature stopped at $x\ensuremath{\approx}$ 0.2, corresponding to the disappearance of the nematic transition. Our result suggests that the increase in the coherent carrier density induced by the suppression of the nematic transition gives rise to the enhancement of ${T}_{\mathrm{c}}$. The decrease in ${T}_{\mathrm{c}}$ with further Te substitution likely arises from too strong electronic correlations, which are not favorable for superconductivity.

Origin of charge density wave in the kagome metal CsV3Sb5 as revealed by optical spectroscopy

We report on a detailed study of the optical properties of CsV$_{3}$Sb$_{5}$ at a large number of temperatures above and below the charge-density-wave (CDW) transition. Above the CDW transition, the low-frequency optical conductivity reveals two Drude components with distinct widths. An examination of the band structure allows us to ascribe the narrow Drude to multiple light and Dirac bands, and the broad Drude to the heavy bands near the $M$ points which form saddle points near the Fermi level. Upon entering the CDW state, the opening of the CDW gap is clearly observed. A large portion of the broad Drude is removed by the gap, whereas the narrow Drude is not affected. Meanwhile, an absorption peak associated with interband transitions near the saddle points shifts to higher energy and grows in weight. These observations are consistent with the scenario that the CDW in CsV$_{3}$Sb$_{5}$ is driven by nesting of Fermi surfaces near the saddle points at $M$.

Optical and hidden transport properties of BaFe1.91Ni0.09As2 film

Optical spectroscopy was used to study the electrodynamics and hidden transport properties of a BaFe1.91Ni0.09As2 thin superconducting (SC) film. We analyzed the normal state data using a Drude–Lorentz model with two Drude components: one narrow (D1) and another broad one (D2). In the SC state, two gaps with –2.0 and –4.3 are formed from the narrow component D1 while the broad component D2 remains ungapped. The calculated total DC resistivity of the film and the low-temperature scattering rate for the narrow Drude component show a hidden Fermi-liquid behavior. The change of total electron–boson coupling (λ tot) and representative energy (Ω0) in the normal state with respect to the SC state is typical of other iron-based materials as well as high-temperature superconducting (HTSC) cuprates.

Spin-Reorientation-Induced Band Gap in Fe_{3}Sn_{2}: Optical Signatures of Weyl Nodes.

Temperature- and frequency-dependent infrared spectroscopy identifies two contributions to the electronic properties of the magnetic kagome metal Fe_{3}Sn_{2}: two-dimensional Dirac fermions and strongly correlated flat bands. The interband transitions within the linearly dispersing Dirac bands appear as a two-step feature along with a very narrow Drude component due to intraband contribution. Low-lying absorption features indicate flat bands with multiple van Hove singularities. Localized charge carriers are seen as a Drude peak shifted to finite frequencies. The spectral weight is redistributed when the spins are reoriented at low temperatures; a sharp mode appears suggesting the opening of a gap due to the spin reorientation as the sign of additional Weyl nodes in the system.

The effect of oblique-angle sputtering on large area deposition: a unidirectional ultrathin Au plasmonic film growth design

Growing ultrathin nanogranular (NG) metallic films with continuously varying thickness is of great interest for studying regions of criticality and scaling behaviors in the vicinity of quantum phase transitions. In the present work, an ultrathin gold plasmonic NG film was grown on a sapphire substrate by RF magnetron sputtering with an intentional deposition gradient to create a linearly variable thickness ranging from 5 to 13 nm. The aim is to accurately study the electronic phase transition from the quantum tunneling regime to the metallic conduction one. The film structural characterization was performed by means of high-resolution transmission electron microscopy, atomic force microscopy, as well as x-ray diffraction and reflectivity techniques, which indicate the Volmer–Weber film growth mode. The optical and electrical measurements show a transition from dielectric-isolated gold NPs towards a continuous metallic network when t becomes larger than a critical value of tM = 7.8 nm. Our results show that the onset of the percolation region occurs when a localized surface plasma resonance transforms to display a Drude component, indicative of free charge carriers. We demonstrate that, by using a continuously varying thickness, criteria for metallicity can be unambiguously identified. The onset of metallicity is clearly distinguished by the Drude damping factor and by discontinuities in the plasma frequencies as functions of thickness.

Drag viscosity of metals and its connection to Coulomb drag

Recent years have seen a surge of interest in studies of hydrodynamic transport in electronic systems. We investigate the electron viscosity of metals and find a new component that is closely related to Coulomb drag. Using the linear response theory, viscosity, a transport coefficient for momentum, can be extracted from the retarded correlation function of the momentum flux, i.e., the stress tensor. There exists a previously overlooked contribution to the shear viscosity from the interacting part of the stress tensor which accounts for the momentum flow induced by interactions. This contribution, which we dub drag viscosity, is caused by the frictional drag force due to long-range interactions. It is therefore linked to Coulomb drag which also originates from the interaction induced drag force. Starting from the Kubo formula and using the Keldysh technique, we compute the drag viscosity of 2D and 3D metals along with the drag resistivity of double-layer 2D electronic systems. Both the drag resistivity and drag viscosity exhibit a crossover from quadratic-in-T behavior at low temperatures to a linear one at higher temperatures. Although the drag viscosity appears relatively small compared with the normal Drude component for the clean metals, it may dominate hydrodynamic transport in some systems, which are discussed in the conclusion.

Crystallization of optically thick films of CoxFe80−xB20 : Evolution of optical, magneto-optical, and structural properties

CoFeB alloys are highly relevant materials for spintronic applications. In this work, the crystallization of CoFeB alloys triggered by thermal annealing was investigated by x-ray diffraction techniques and scanning electron microscopy, as well as spectroscopic ellipsometry and magneto-optical Kerr effect spectroscopy for annealing temperatures ranging from 300 to ${600}^{\ensuremath{\circ}}\mathrm{C}$. The transformation of \ensuremath{\sim}100-nm-thick ${\mathrm{Co}}_{x}{\mathrm{Fe}}_{(80\ensuremath{-}x)}{\mathrm{B}}_{20}$ films from amorphous to polycrystalline was revealed by the sharpening of spectral features observed in optical and magneto-optical dielectric functions spectra. The influence of B on the dielectric function was assessed both experimentally and by optical modeling. By analyzing the Drude component of the optical dielectric function, a consistent trend between the charge-carrier scattering time/resistivity and the annealing temperature was observed, in agreement with the electrical investigations by means of the four-point-probe method.

Optical and photoemission investigation of structural and magnetic transitions in the iron-based superconductor Sr0.67Na0.33Fe2As2

We report the temperature-dependent optical conductivity and ARPES studies of the iron-based superconductor (SC) Sr$_{0.67}$Na$_{0.33}$Fe$_2$As$_2$ in the high-temperature tetragonal paramagnetic phase; below the structural and magnetic transitions at $T_{\rm N}\simeq$125 K in the orthorhombic spin-density-wave (SDW)-like phase, and $T_r\simeq$42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDW order exist; and below the SC transition at $T_c\simeq$10 K. The free-carrier component in the optical conductivity is described by two Drude contributions; one strong and broad, the other weak and narrow. The broad Drude component decreases dramatically below $T_{\rm N}$ and $T_r$, with much of its strength being transferred to a bound excitation in the mid-infrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone-folding below $T_r$. Below $T_c$ the dramatic decrease in the low-frequency optical conductivity signals the formation of a SC energy gap. ARPES reveals hole-like bands at the center of the Brillouin zone (BZ), with both electron- and hole-like bands at the corners. Below $T_{\rm N}$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; while below $T_r$ the electron-like bands shift and split, giving rise to a low-energy excitation in the optical conductivity at ~20 meV. The magnetic states, with resulting SDW and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets, but appears to have relatively little impact on the SC in this material.

Contrasting pressure evolution of f -electron hybridized states in CeRhIn5 and YbNi3Ga9 : An optical conductivity study

Optical conductivity [$\sigma(\omega)$] of CeRhIn$_5$ and YbNi$_3$Ga$_9$ have been measured at external pressures to 10 GPa and at low temperatures to 6 K. Regarding CeRhIn$_5$, at ambient pressure the main feature in $\sigma(\omega)$ is a Drude peak due to free carriers. With increasing pressure, however, a characteristic mid-infrared (mIR) peak rapidly develops in $\sigma(\omega)$, and its peak energy and width increase with pressure. These features are consistent with an increased conduction ($c$)-$f$ electron hybridization at high pressure, and show that the pressure has tuned the electronic state of CeRhIn$_5$ from very weakly to strongly hybridized ones. As for YbNi$_3$Ga$_9$, in contrast, a marked mIR peak is observed already at ambient pressure, indicating a strong $c$-$f$ hybridization. At high pressures, however, the mIR peak shifts to lower energy and becomes diminished, and seems merged with the Drude component at 10 GPa. Namely, CeRhIn$_5$ and YbNi$_3$Ga$_9$ exhibit some opposite tendencies in the pressure evolutions of $\sigma(\omega)$ and electronic structures. These results are discussed in terms of the pressure evolutions of $c$-$f$ hybridized electronic states in Ce and Yb compounds, in particular in terms of the electron-hole symmetry often considered between Ce and Yb compounds.

Unravelling the mechanism of the semiconducting-like behavior and its relation to superconductivity in (CaFe1−xPtxAs)10Pt3As8

The temperature-dependence of the in-plane optical properties of (CaFe$_{1-x}$Pt$_{x}$As)$_{10}$Pt$_{3}$As$_{8}$ have been investigated for the undoped ($x=$0) parent compound, and the optimally-doped ($x=$0.1) superconducting material ($T_{c}\simeq$ 12 K) over a wide frequency range. The optical conductivity has been described using two free-carrier (Drude) components, in combination with oscillators to describe interband transitions. At room temperature, the parent compound may be described by a strong, broad Drude term, as well as a narrow, weaker Drude component. Below the structural and magnetic transitions at $\simeq$ 96 and 83 K, respectively, strength is transferred from the free-carrier components into a bound excitation at $\simeq$ 1000 cm$^{-1}$, and the material exhibits semiconducting-like behavior. In the optimally-doped sample, at room temperature the optical properties are again described by narrow and broad Drude responses comparable to the parent compound; however, below $T^\ast \simeq$ 100 K, strength from the narrow Drude is transferred into a newly-emergent low-energy peak at $\simeq$ 120 cm$^{-1}$, which arises from a localization process, resulting in semiconducting-like behavior. Interestingly, below $T_{c}$, this peak also contributes to the superfluid weight, indicating that some localized electrons condense into Cooper pairs; this observation may provide insight into the pairing mechanism in iron-based superconductors.

Band-selective clean-limit and dirty-limit superconductivity with nodeless gaps in the bilayer iron-based superconductor CsCa2Fe4As4F2

The optical properties of the new iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_c \sim 29$~K have been determined. In the normal state a good description of the low-frequency response is obtained with a superposition of two Drude components of which one has a very low scattering rate (narrow Drude-peak) and the other a rather large one (broad Drude-peak). Well below $T_c \sim 29$~K, a pronounced gap feature is observed which involves a complete suppression of the optical conductivity below $\sim$ 110~cm$^{-1}$ and thus is characteristic of a nodeless superconducting state. The optical response of the broad Drude-component can be described with a dirty-limit Mattis-Bardeen-type response with a single isotropic gap of $2\Delta \simeq 14$~meV. To the contrary, the response of the narrow Drude-component is in the ultra-clean-limit and its entire spectral weight is transferred to the zero-frequency $\delta(\omega)$ function that accounts for the loss-free response of the condensate. These observations provide clear evidence for a band-selective coexistence of clean- and dirty-limit superconductivity with nodeless gaps in CsCa$_2$Fe$_4$As$_4$F$_2$.

Optical properties of a semi-Dirac material

Within a Kubo formalism, we calculate the absorptive part of the dynamic longitudinal conductivity $\sigma(\Omega)$ of a 2D semi-Dirac material. In the clean limit, we provide separate analytic formulas for intraband (Drude) and interband contributions for $\sigma(\Omega)$ in both the relativistic and nonrelativistic directions. At finite doping, in the relativistic direction, a sumrule holds between the increase in optical spectral weight in the Drude component and that lost in the interband optical transitions. For the nonrelativistic direction, no such sumrule applies. Results are also presented when an energy gap opens in the energy dispersion. Numerical results due to finite residual scattering are provided and analytic results for the dc limit are derived. Energy dependence and possible anisotropy in the impurity scattering rate is considered. Throughout, we provide comparison of our results for $\sqrt{\sigma_{xx}\sigma_{yy}}$ with the corresponding results for graphene. A generalization of the 2D Hamiltonian to include powers of higher order than quadratic (nonrelativistic) and linear (relativistic) is considered. We also discuss the modifications introduced when an additional flat band is included via a semi-Dirac version of the $\alpha$-${\cal T}_3$ model, for which an $\alpha$ parameter tunes between the 2D semi-Dirac (graphene-like) limit and the semi-Dirac version of the dice or ${\cal T}_3$ lattice.