Frequency dependence of the conductivity

Fig. 6.19 Frequency dependence of the conductivity at different temperatures for a micro PS film (5 U cm p-type, 30 mA cmf2, ethanoic HF). The transition from a frequency regime...

The frequency dependence of the conductivity is also a signature of disorder. Here again, the behavior commonly observed in CPs is similar to that in other disordered solids. Namely, after a plateau where o-(o>) = o"dC, ) increases as a power law of frequency ... 

Several experimental results show that the intermediate regime 10 K<7 <7] behaves as a very unusual anisotropic 2-D metal. As revealed by optical data in all Se-based salts, there still exists at T= 20 K a clear-cut gap in the frequency dependence of the conductivity, 2Ap = 200 cm [93]. 

It was shown in Refs. 91 and 92 that ring-shaped structures (ring clusters) generate double peaks in the frequency dependence of the conductivity. Such ring structures in the system at hand are located chaotically and hierarchically, in a self-similar way, and also lead to peaks in the conductivity. 

In this paper we investigate the dynamics of impurity pinning of the charge density wave (CDVJ) and the frequency dependence of the conductivity in the one-dimensional Peierls=... 

At lower temperatures (<170°C), electrical conduction in sulfur is thought to take place primarily by the electrophoresis of impurities, and the conductivity shows a direct correlation with the viscosity (J). With increasing temperature electronic conduction becomes predominant, and the conductivity shows a linear dependence of log k upon 1/T ( °K). This behavior is characteristic of, but not limited to, intrinsic semiconductors. The observed frequency dependence of the conductivity is in the opposite direction of that expected if electronic conduction occurs by a Tiop-ping mechanism (10), The activation energy does not show a dependence upon temperature which is characteristic of this type of mechanism, although such an eflFect may not be evident over the relatively short temperature range of the measurements. 

Fig. 7. Frequency dependence of the conductivity of the weakly coupled paired holon superconductor (X = 0.1). The excitation spectrum is gapless at T = 0.

The frequency dependence of the conductivity of K2Pt(CN)4Bro.3o(H20)3, Fig. 32, has been determined (456) by a Kramers-Kronig analysis of the... 

Fig. 20. Frequency dependence of the conductivity of He+-irradiated single crystals of YBa2Cu30 95. Upper curves in all panels were measured at temperatures slightly above T, while the lower curves were obtained at 10 K. The dashed curves show the fit of the narrow normal component in the superconducting conductivity to the Drude formula. After Basov et al. (1994b).

Carbotte et al. (1995) analyzed the complex conductivity in the presence of disorder in the weak Bom-scattering limit assuming different symmetries of the order parameter. Their main result is that the data presented in fig. 20 are not consistent with an s-wave gap but can be qualitatively accounted for within a d-wave model. In particular, disordered d-wave superconductors are expected to reveal an enhancement of the spectral weight of the normal component in the superconducting state response. The frequency dependence of the conductivity at T and its evolution with disorder are remarkably similar in the experimental data by Basov et al. (1994b) and in theoretical calculations by Jiang et al. (1996). 

More can be learned when going to higher frequencies than those of microwaves. Figure 1.47 shows the frequency dependence of the conductivity of a polyacetylene sample doped with AsFs, measured in the entire frequency regime from d.c. up to terahertz (submillimeter waves, at room temperature) [103]. To cover such a wide frequency range, five different experimental methods had to be applied four-probe... 

Figure 1.47. Frequency dependence of the conductivity of 0.7% AsFs-doped cw-polyacetylene at 300 K in the frequency range from d.c. to far-infrared. (Reprinted with permission from ref 103)...

Figure 6. The frequency dependence of the conductivity of HAT6/NOBF4 (1 mol%) in the Col, phase at 360 K.

A more extended study of the frequency dependence of the conductivity is shown in Fig. 13, where dc, microwave and IR data are combined /10/. The experimental curve (solid line) is tentatively decomposed into a free carrier contribution following a Drude behaviour O = aQ/(1+03 T ), and a hopping contribution. 

The present formalism for the admittance is quite general and applicable to various quantities. As a representative example, we shall consider the ac conductivity, due to hopping which is governed by the master equation (50) with several kinds of distributions of Wg g,. We are interested in the frequency dependence of the conductivity ( ). Since O ( ) always bears a factor ne a wg/kT, one is concerned w,ith the dimensionless ac conductivity CT (w) (O) /(ne w /kT) or... 

Where t= l/2j = characteristic relaxation time, (o = radial frequency, N = parameter that defines the frequency dependence of the conductivity term (typically N - 1 and equals the slope of the low-frequency increase in e or e" plot due to the low-frequency conduction through the system, as shown in Figure 1-4B), a and p = shape parameters accounting for symmetric and asymmetric broadening of the relaxation peak. 

Fig. 3.2 (a) Schematic of the cells used for the chemical doping studies of conducting liquid crystals (b) the frequency dependence of the conductivity of HAT6 doped with 0.5 mol% of aluminium trichloride in the Coli, phase (parallel and perpendicular to the axis of the column)... 

In the inhomogeneous material with conducting grains embedded in an insulating matrix, below the percolation threshold, one can expect due to the Maxwell-Wagner effect strong frequency dependence of the conductivity ... 

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