Drude behavior

The main goal of optical studies is to determine to what extent the law given by Eq. (33), namely the Drude behavior, is followed for onedimensional conductors in the presence of strong correlations. Figure 26 gives a typical example of Drude behavior taken from the work of Jacobsen [95]. 

Fig. 3. Idealized Cotton effect at an isolated, optically active absorption band with its maximum at X<. If the positive limb of the rotatory dispersion is to the high wavelength side of the band, the Cotton effect is termed positive if the negative limb is at higher wavelength, the effect is negative. In regions distant from the absorption band, the rotatory dispersion approaches simple Drude behavior.

The argument, just briefly outlined, show that, in a quarter-filled system, the presence of strong on-site correlations leads to deviations of the optical properties fi om the Drude behavior [3] expected for independent electrons. Such deviations are not as large, as those predicted for a half-filled system, and, in particular, do not relate directly to U itself, but, rather, to dimeric lattice distortions and, possibly, to the nearest-neighbor repulsion V. 

Double-gate FET structure, 16-20 Double-gate, 16-20-16-21 Drude behavior, 15-50... 

From the experimental data which exist for current systems, estimates of the intrinsic conductivity also can be made [197]. The intrinsic Drude nature of metallic carriers has been identified using both microwave and optical techniques. Both of these techniques have identified the presence of a group of carriers which demonstrate Drude behavior with a long scattering time (t 10-"s). The Drude conductivity for traditional metals is given by... 

T = ne rlm. In the present systems, only a small fraction ( 0.1%) of the conduction electrons show this Drude behavior. If all of the conduction electrons (determined by doping percentage) have a scattering time equivalent to T 10 " S, then O-ulUmate lO S/cm. 

Even if we associate free electrons with wave packets, there are still problems with the Drude model. One is that the electrons in reality are subject to the Fermi-Dirac statistics. As T 0, the Drude behavior of conductivity is not the correct one. The Drude model, invented long before quantum mechanics, does not even distinguish between insulators and conductors. Inert gases would be conductors, since in classical models any small increase in energy should be possible. This is not the case in quantum mechanics, of course, and this is consistent with the fact that diamond and silicates are insulators at T = 0. 

The implications of the reflectivity spectra become clear when the optical conductivity, a-(a>), is obtained through the Kramers-Kronig transformation. Figure 151 shows o(w) over the spectral range below 1.5 eV [1160]. Although the results imply intraband Drude-like excitations centered at w = 0 (there is no energy gap), the optical conductivity deviates from the normal Drude behavior at low energies below about 0.2 eV, o(q)) decreases toward... 

In spite of the characteristic metallic signatures in the reflectance spectra, however, the corresponding (t(w) are not typical of a good metal, as with PANI-CSA. Even for the metallic regime, a(a)) deviates considerably from the normal Drude behavior below 0.4 eV in contrast to Drude behavior, o(w) is suppressed as w -> 0. This decrease in o( j) also arises from weak localization, as demonstrated in PANI-CSA [1160, 1161]. For the insulating regime, however, o(a ) is suppressed even more at low frequencies, indicating that the states near in the conduction band are localized. This localization arises from disorder in the context of Anderson localization [1125,1156,1157]. 

Q.p = 9970 cm-1 (1.17 eV), 1/t = 4340 cm- (0.51 eV), and fcf A = 1.6 with an assumption of C = 1. These parameters are reasonable. The plasma frequency is close to that obtained from the reflectance minimum ( 1.4 eV) and the peak in the loss function ( 1.1 eV). The value of fcf A (= 1.6) indicates that PANI-CSA is not a good metal [1160]. Instead, this fact supports that PANI-CSA is on the metal-insulator boundary and approaching the loffe-Regel limit. Moreover, the deviations from simple Drude behavior in the far-IR are quantitatively consistent with the LMD model [1160, 1161]. As indicated by Eq. (4.18), localization depresses o(w) below the Drude curve in the far-IR. 

Upon protonation and conversion to the emeraldine salt, qualitative changes in the spectra are evident the 1.8-eV peak disappears and the amplitude of the 3.7-eV peak decreases. Two new features develop for both PANI-CSA and PANI-H2SO4. For PANI-CSA, (j(to) has a sharp peak at 2.7 eV and increases mono-tonically with decreasing frequency, reaching a maximum in the IR at around 0.2 eV. Although the low-frequency spectral response is attributable to the intraband excitations (free carriers in the conduction band), deviations from the normal Drude behavior are observed at the lowest frequencies, as discussed in the previous section [1160]. Below 0.2 eV, o(w) is suppressed toward the dc value from weak localization due to disorder [1160]. In contrast, for PANI-H2SO4, o (o) has a broad maximum at 1 eV and decreases rapidly with frequency in the IR. 

Fig. 190. Real part of the a.c. conductivity x (o)) of stoichiometric TmSe versus photon energy. The dotted line indicates a simple Drude behavior. The d.c. values are also given for 3, 77, and 300 K.

Figure 6.23. Far-IR reflection spectrum of K3C60. Drude behavior indicating metallic prop es is observed. (Reproduced by permission from ref 119. Copyright 1992, American Physical Society.)...

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