Disordered metallic regime

In a disordered metallic regime the conductivity at low temperature is generally expressed by... 

Among the previous generation conducting polymers, metallic behavior with finite conductivity at millikelvin (mK) temperatures was observed only in doped polyacetylene. Gould et al. [41] and Thummes et al. [73,74] carried out temperature and magnetic field dependence studies of the conductivity in doped (CH)., down to millikelvin temperatures. Contributions from both weak localization and e-e interactions were observed in the disordered metallic regime. In doped PPV samples, Madsen et al. [99] also observed the e-e interaction contribution to conductivity (a oc p ) in metallic samples. 

Log-log plots of W vs. 7precisely identify the metallic regime. If the temperature coefficient of W is positive, then the conductivity in the disordered metallic regime at low temperatures is expressed by [42-44]... 

Figure 7.5. An electronic phase diagram illustrating the location of a metallic regime, at low U (Coulomb repulsion energy) and B (disorder), where dp/dT > 0. With increasing U and/or B. the system becomes nonmetallic (dp/dT< 0) but may still exhibit Pauli paramagnetism if there is no band gap U B).

Transport studies [46,1136] on this system have been successful in characterizing the extent of disorder in terms of the temperature dependence of the resistivity, p(.T), more specifically, the resistivity ratio, pr = p(1.4 K)/p(300 K), and classified the materials into the metallic regime, the critical regime, and the insulating regime as explained previously. 

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]. 

On the contrary, the optical spectra for the metallic regime indicate delocalized electronic states near Ef, as already explained in the previous section. Thus, on the metallic side of the M-I transition, PPy-PFg is a disordered metal and can be described well by the LMD model [1162], while, on the insulating side, PPy-PF5 is characterized as a Fermi glass, which is attributed to disorder in the context of Anderson IcKaliza-tion. 

Measurements of p(7) for a sample close to the critical point were extended down to 20 mK in order to identify the transition from the critical regime to either the insulating or metallic regime (depending upon the extent of disorder in the sample). As shown in Fig. 2.8, the power law dependence persists down to 0.4 K, below which a resistivity increase toward insulating behavior is observed. 

The room temperature conductivity increases up to 4 kbar and then gradually decreases at higher pressures. At 8 kbar. the temperature dependence of cri and o-j. have decreased by factors of 1.4 and 1.6, respectively, indicating that interchain transport is enhanced by pressure. W T) is temperature-independent from 180 to 60 K in directions both parallel and perpendicular to the chain axis, indicating that at ambient pressure I-(CH)x is on the metallic side of the critical regime. At 8 kbar, the system exhibits more metallic behavior due to enhanced interchain transport. The a(T) dependence (4-50 K) indicates that inelastic e-e scattering in disordered metals is the dominant scattering process. 

For metallic PANI-CSA, the conductivity at 20 mK is approximately 30 S/cm. the positive TCR extends from 300 to 150 K. and pr < 2. In this metallic regime, the dependence at low temperatures points to the importance of e-e interactions. The magnitude of the inelastic scattering time, t, -= 10 s, is typical of that of amorphous metals. The intrinsic conductivity of PANI-CSA along the chain axis is estimated to be significantly greater than 10 S/cm at room temperature. The magnetic and optical properties also indicate that PANI-CSA is a disordered metal. 

As for the other conducting polymers, pr can be used to quantify the disorder as the disorder decreases in PPy-PF6, Pr decreases systematically, with the M-I transition at Pr = 10. The resistivity at high temperatures follows the power law temperature dependence with the power law exponent p decreasing from I to 0.3 as pr decreases. As the system approaches the transition from the metallic regime (pr 1-6) ... 

As in the critical and metallic regimes, the extent of disorder can be characterized in terms of the resistivity ratio [120]. The approximate pr values for the insulating regime are the following [172] ... 

The temperature dependence of the resistivity of PANI-CSA is sensitive to the sample preparation conditions. This is clearly shown in the W vs. T plots, e.g., as in Fig. 2.49. The resistivity ratio for PANI-CSA is typically less than 50 in the metallic regime (pr < 3), p(T) approaches a finite value as 7—> 0 [151] in the critical regime (p, 3), p T) follows power law dependence and in the insulating regime (pr > 4),p(7 ) follows Eq. (15) (Mott VRH conduction) with VRH exponent a = 0.25 0.3 and n = 10 -10 The Mott to ES VRH crossover noted for PPy-Pp6 and PATs has not yet been clearly observed in PANI-CSA. The systematic variation from the critical regime to the VRH regime as the value of Pr increases from 2.94 to 4.4 is shown beautifully in the W vs. T plot of Fig. 2.49. This is a classical demonstration of the role of disorder-induced localization in doped conducting polymers. 

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