Drude behavior in the far-infrared conductivity of cuprate superconductors

Liu, Hsiang Lin; Quijada, Manuel A.; Romero, D. B.; Tanner, D. B.; Zibold, A.; Carr, G. L.; Berger, H.; Forró, Lászlø; Mihály, L.; Cao, G.; Beom‐Hoan, O; Markert, J. T.; Rice, J. P.; Burns, Michael J.; Delin, K. A.

doi:10.1002/andp.200510205

Cited by 8 publications

(10 citation statements)

References 40 publications

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“…λ for the one-electron exchange reaction. This is consistent with the well-resolved data for YBa 2 Cu 3 O 7 [20][21][22][23]47,48].…”

Section: Discussionsupporting

confidence: 91%

“…Equation 4 is the MMCT transfer transition at hν = 2.0 eV [19]. In the optimally doped system, there is a minimum in the far infrared optical conductivity at about 300 cm −1 in [20][21][22][23] and La 2−x Sr x CuO 4 [9], probably due to the SC gap. For 800>ν>300 cm −1 , the absorption is due to (4) since it cannot be due to (2), which is independent of doping and at 0.135 eV (∼ 1100 cm −1 ) [14].…”

Section: Introductionmentioning

confidence: 99%

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Conductivity in Cuprates Arises from Two Different Sources: One-Electron Exchange and Disproportionation

Larsson

2016

J Supercond Nov Magn

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Simulation of the resistivity in the normal state of doped La 2−x Sr x CuO 4 has been performed using a hopping model based on Marcus theory. The results are in substantial agreement with experimental results. At oxidative doping, Cu(III) sites are formed and electron mobility possible due to hopping: Cu(III)Cu(II) → Cu(II)Cu(III) (one-electron exchange). In the underdoped, non-metallic region, the resistivity (ρ) decreases from almost insulation at T = 0 to a minimum at about T = 100 K. ρ then increases more than linearly with T (∼ T 3/2 ) in the region 100 < T < 500 K. A photo-induced metal-metal (MM) charge transfer transition at 2 eV 2Cu(II) + hν → Cu(I) + Cu(III) is responsible for the strong absorption in the visible spectrum of La 2 CuO 4 . The down-shift of spectral density with doping (x) in La 2−x Sr x CuO 4 depends on the appearance of Cu(III) sites which makes optical as well as thermal one-electron exchange transitions possible with lower energy. Disproportionation occurs spontaneously for x > 0.06, opening up for electron pair formation. Configuration interaction between two-electron states of low chemical potential, but strong vibrational coupling, gives rise to the superconductor and pseudogaps. Data from photo-induced conductivity and absorption spectra are used in the simulation, which gives results in good agreement with experiments. Possible explanations for Raman and MIR absorption suggest themselves.

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“…λ for the one-electron exchange reaction. This is consistent with the well-resolved data for YBa 2 Cu 3 O 7 [20][21][22][23]47,48].…”

Section: Discussionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Conductivity in Cuprates Arises from Two Different Sources: One-Electron Exchange and Disproportionation

Larsson

2016

J Supercond Nov Magn

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“…1a–f. Although similar information could be obtained through reflectance measurements [22], the reason we consider transmission measurements in this work (Fig. 1a) is to avoid potential experimental systematic errors.…”

Section: Resultsmentioning

confidence: 99%

A Drude model analysis of conductivity and free carriers in boron-doped diamond films and investigations of their internal stress and strain

Manciu

Durrer

et al. 2014

J Mater Sci

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Boron-doped diamond (BDD) has seen a substantial increase in interest for use as electrode coating material for electrochemistry and studies of deep brain stimulation mechanism. In this study, we present an alternative method for determining important characteristics, including conductivity, carrier concentration, and time constant, of such material by the signature of Drude-like metallic behavior in the far-infrared (IR) spectral range. Unlike the direct determination of conductivity from the four-point probe method, using far-IR transmittance provides additional information, such as whether the incorporation of boron results in a large concentration of carriers or in inducing defects in the diamond lattice. The slightly doped to medium-doped BDD samples that were produced using chemical vapor deposition and analyzed in this work show conductivities ranging between 5.5 and 11 (Ω cm)−1. Different growth conditions demonstrate that increasing boron concentration results in an increase in the carrier concentration, with values between 7.2 × 1016 and 2.5 × 1017 carriers/cm3. Addition of boron, besides leading to a decrease in the resistivity, also resulted in a decrease in the time constant, limiting BDD conductivity. Investigations, by confocal Raman mapping, of the induced stress in the material due to interaction with the substrate or to the amount of doping are also presented and discussed. The induced tensile stress, which was distributed closer to the film-substrate interface decreased slightly with doping.

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“…The ratio, T(ω), of the transmission of radiation of angular frequency ω through a thin conductive film deposited on a substrate, T C (ω), to the transmission through the substrate alone, T S (ω), without consideration of multiple reflections is given by [31,32]:

normalT (ω) \equiv \frac{T_{C} (ω)}{T_{S} (ω)} = \frac{1}{{| 1 + \frac{sans-serifσ (ω) Z_{0} normald}{n_{S} + 1} |}^{2}}

where σ(ω) is the conductivity, Z 0 = 377 Ω is the impedance of free space, d is the thickness of the thin film, and n S is the index of refraction of the substrate (in this case, for Si, n s = 3.4). The thicknesses of the samples used were about 1 µm for HOPG, 9.4 nm for multi-layer graphene, and 1.7 nm for the sample containing a mixture of single-layer and few-layer graphene.…”

Section: Methodsmentioning

confidence: 99%

“…We also present and discuss an alternative method to study the conductivity of graphene using the Drude model. This model has been successfully applied to such an analysis for metallic thin films [ 31 , 32 ] and, very recently, for carbon based materials [ 33 , 34 , 35 , 36 ]. Two types of optical transitions (e.g., intraband and interband) are known to contribute to absorption in graphene.…”

Section: Introductionmentioning

confidence: 99%

Raman and Conductivity Analysis of Graphene for Biomedical Applications

et al. 2016

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In this study, we present a comprehensive investigation of graphene’s optical and conductive properties using confocal Raman and a Drude model. A comparative analysis between experimental findings and theoretical predictions of the material’s changes and improvements as it transitioned from three-dimensional graphite is also presented and discussed. Besides spectral recording by Raman, which reveals whether there is a single, a few, or multi-layers of graphene, the confocal Raman mapping allows for distinction of such domains and a direct visualization of material inhomogeneity. Drude model employment in the analysis of the far-infrared transmittance measurements demonstrates a distinct increase of the material’s conductivity with dimensionality reduction. Other particularly important material characteristics, including carrier concentration and time constant, were also determined using this model and presented here. Furthermore, the detection of micromolar concentration of dopamine on graphene surfaces not only proves that the Raman technique facilitates ultrasensitive chemical detection of analytes, besides offering high information content about the biomaterial under study, but also that carbon-based materials are biocompatible and favorable micro-environments for such detection. Such information is valuable for the development of bio-medical sensors, which is the main application envisioned for this analysis.

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Drude behavior in the far-infrared conductivity of cuprate superconductors

Cited by 8 publications

References 40 publications

Conductivity in Cuprates Arises from Two Different Sources: One-Electron Exchange and Disproportionation

Conductivity in Cuprates Arises from Two Different Sources: One-Electron Exchange and Disproportionation

A Drude model analysis of conductivity and free carriers in boron-doped diamond films and investigations of their internal stress and strain

Raman and Conductivity Analysis of Graphene for Biomedical Applications

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