Drude peak

Among many fascinating properties, quasicrystals with high structural quality, such as the icosahedral AlCuFe and AlPdMn alloys, have unconventional conduction properties when compared with standard intermetallic alloys. Their conductivities can be as low as 450-200 (Qcm) [7]. Furthermore the conductivity increases with disorder and with temperature, a behaviour just at the opposite of that of standard metal. In a sense the most striking property is the so-called inverse Mathiessen rule [8] according to which the increases of conductivity due to different sources of disorder seems to be additive. This is just the opposite that happens with normal metals where the increases of resistivity due to several sources of scattering are additive. Finally the Drude peak which is a signature of a normal metal is also absent in the optical conductivity of these quasicrystals. 

Fig. 22 Infrared reflectivity of a powder sample of Na2CsC60. A Lorentz Drude peak is shown for 20 and 200 K but at 300 K, the metallic behavior is lost. (From [55])...

The characteristic composite behavior of (t maM for medium consisting of spherical particles with volume fractions / of Drude conductor and 1 - / of insulator is shown in Figure 15.5. For a volume fraction / less than the percolation value (/ = 1/3 for spheres), (Tema (impurity band of localized plasmon-like excitations. As the system approaches the percolation threshold, the localized peak o-ema(w) shifts to lower frequency. Above the percolation threshold, a Drude peak corresponding to the carriers that have percolated through the composite structure occurs at low frequency. Only a fraction ( (3/— l)/2 [119]) of the full conduction electron plasma frequency appears in the Drude peak, depending on the proximity to the percolation threshold. The same percolating free electron behavior is observable in the dielectric response ema(w) for the system. 

Fig. 3.5 Schematic (t (o) for an insulator-metal composite made up of volume fractions /of a Drude metal and 1 - / of an insulator, as calculated in the effective medium theory. The heavy line at w = 0 represents the Drude peak. The integrated stength of the delta function is proportional to the height of the delta function. The scattering time is chosen to be very long so that the width of the Drude peak is too narrow to be resolved in the plot, emphasizing the behavior of the localized modes. (From Ref. 88.)...

Fig. 11. The Bruggeman model (BM) lakes into account the modification of the effective medium by the adjunction of metal in the medium. The net effect is a broadening of the resonance peak. The parameters of the metallic spheres in these calculations are fuHp = I eV and fiV = 0.1 eV. The insulating host is defined by ftcOp i = 1 eV and ftf = 1 eV and fidiy = 20 eV. Note that the normal Drude curve is superimposed with the Bruggeman curve with/= 1.

Below the plasma frequency at about 15 eV the only appreciable deviation from Drude theory occurs near 1.5 eV, where interband electronic transitions produce a peak in t" and associated structure in c with this exception, c for aluminum goes monotonically toward negative infinity and c" toward positive infinity as the energy approaches zero. 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

Fig. 15 Optical conductivity of K3C60 and K4C60 illustrating the disappearance of the Drude term in K4C60. The peak at 1 eV is due to interband transitions. The strong peak at 0.5 eV in K4C60 corresponds to the gap seen by transport. (From [38])...

Spectroscopic measurements, such as electron energy loss spectroscopy (EELS), infrared (IR) and Raman spectroscopy, can probe the very small energy excitations across the Fermi level (Ef) or band gap by changes in the peak shape such as via the Drude tail in photoemission. However, such lines-shape changes can also be caused by a number of experimental effects making these measurements difficult. 

The Drude-like peak may be attributed to the coherent motion of doped-holes. This assignment is based on the assumption that the conventional transport theory is applicable in the cuprate although a number of experiments indicate that metallic... 

The mid-IR peak has been explained due to the small polaron formation since the early days of the cuprate research. A support for this assignment is the photoinduced conductivity measurement [4] the photoinduced conductivity in LSCO (Fig. 4) shows a very similar peak to the mid-IR peak of the optical conductivity in the V = 0.02 sample. It is also qualitatively explained by the small polaron transport theory [4]. However, this mid-IR peak assignment contradicts the assignment that the Drude-like peak is due to the coherent motion of holes since the former assumes that the hole-lattice interaction is so strong that doped holes become small polarons, while the latter does opposite. Therefore, if we assign that the mid-IR peak is due to small polaron formation, we have to abandon the assignment that the Drude-like peak is due to the coherent motion of doped-holes. 

The SPR is then also called Mie resonance. For simple metals, the SPR absorption band has a Lorentzian shape peaked at oi p, the width of which is directly proportional to the collision constant E introduced in the Drude description of the metal dielectiic constant (Eq. 2). Of course, for noble metals the absorption due to interband transitions has to be taken into account in order to obtain the complete spectrum. 

Absorption spectroscopy in the vacuum ultraviolet shows a strong band at 141-143 nm with normal paraffins and another at about 157 nm in isobutane and neopentane. A third band at 128-134 nm is prominent in all of these hydrocarbons as well. Cyclopropane shows bands at 162, 145 and, very strongly, at 124 nm, while cyclobutane shows end absorption up to 185 nm and peaks at 152, 142 and 126 nm. There is a reasonable probability that these are the bands indicated by the Drude expressions and, therefore, that they control the optical activity of saturated hydrocarbons in the quartz ultraviolet and visible. For trans-1,2-dimethylcyclopropane CD measurements down to 150 nm show one Cotton effect at 190 nm and two of opposite... 

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