Frohlich conductivity

The dielectric function of a metal can be decomposed into a free-electron term and an interband, or bound-electron term, as was done for silver in Fig. 9.12. This separation of terms is important in the mean free path limitation because only the free-electron term is modified. For metals such as gold and copper there is a large interband contribution near the Frohlich mode frequency, but for metals such as silver and aluminum the free-electron term dominates. A good discussion of the mean free path limitation has been given by Kreibig (1974), who applied his results to interpreting absorption by small silver particles. The basic idea is simple the damping constant in the Drude theory, which is the inverse of the collision time for conduction electrons, is increased because of additional collisions with the boundary of the particle. Under the assumption that the electrons are diffusely reflected at the boundary, y can be written... 

Frohlich, K., Machajdik, D., Cambel, V., Luptak, R., Pignard, S., Weiss, F., Baumann, P. and Lindner, J. (2001), Substrate dependent growth of highly conductive Ru02 films. J. De Phys., 11 Prll-77-81. 

Optical study indicates that at low temperatures the low-energy electronic properties of some organic metal-like conductors (e.g., TTF-TCNQ) are dominated by charge density wave (CDW) effects. Frequency-dependent conductivity of TTF-TCNQ, obtained from the IR reflectance, at 25 K displays a double-peak structure with a low-frequency band near 35 cm-1 and a very intense band near 300 cm-1 [45]. The intense band may be ascribed to single-particle transitions across the gap in a 2kF (Peierls) semiconducting state, while the 35-cm-1 band is assigned to the Frohlich (i.e., CDW) pinned mode. Low-temperature results based on the bolometric technique [72,73] (Fig. 15) confirm the IR reflectance data. Such a con-... 

Frohlich (1947) based his calculations on the hypothesis of the energy-level scheme shown in Fig. 6.1, where conduction electrons are derived from impurity levels lying deep (V = 1 eV or more) in the forbidden zone. There is also a set of shallow traps spread below the conduction-band edge (F> AF> kT). In outline, the theory of breakdown is then as follows. In an applied electric field E, energy is transferred directly to the conduction electrons (charge e, mass m) at a rate A = jE, where j is the current density. If we suppose that each electron is accelerated in the field direction for an average time 2r between collisions at which its energy is completely randomised, then the mean drift velocity of the conduction electrons in the field direction... 

Possible enhancement of conductivity by Peierls-Frohlich nodes, including effects of pinning by impurities. The major question as to whether paraconductivity above Tc makes a significant contribution is still open. 

The dynamics of impurity pinning of the charge density wave and the frequency dependence of conductivity are investigated in the one-dimensional Peierls-Frohlich state. 

It was proposed to picture TQ in terms of a Peierls-Frohlich condensation of the conduction electron with a high mean field temperature /3o/, with electronic properties dominated by CDW fluctuations in the domain Tp T Tpm ... 

The BCS and Little models for superconductivity are both based on the formation of pairs of electrons with an effective attractive interaction due to phonons or excitons respectively. Recently, J. Bardeen (8,28) revived a model, originally presented by Frohlich in 1954 (152), as a possible explanation of the reported anomalous conductivity behavior of (TTF)(TCNQ) (97). This model predates the BCS theory and relies on the direct interaction between electrons and the one-dimensional lattice resulting in the formation of charge density waves. The model has also been applied to the one-dimensional metal K2Pt(CN)4Bro.3o(H20)s (72, 457). 

A very important feature of the Frohlich model is that the lattice distortion and the charge density wave need not be fixed to the frame of reference of the lattice (i.e., the phase of the distortion need not be fixed). The electrons which make up the charge density wave may then move as a unit (collective charge transport) with a large effective charge and large effective mass leading to enhanced conductivity. 

Fig. 33. Far infrared to uv reflectivity of K2Pt(CN)4Bro.3o(H20)8 for light polarized parallel to the conducting axis. The dashed line is for the sample at 300°K, the solid line 40 K. The low frequency structure (50cm i) at 40 °K is assigned to the response of a pinned charge density wave (pinned Frohlich mode) (72).

From the values of resistance [K] obtained for the different investigated systems, the dc conductivity was calculated, according to the equation reported in [32] and listed in Table 7.10. After subtracting the dc losses from the measured s" values, the results showed a well-defined absorption region [Fig. 7.3) according to the Frohlich equation [33]. Table 7.11 shows these values in the... 

The blocked or restricted motion of the charges in a body of matter appears to the experimenter as a polarization response. The continuous or semicontinuous motion of such charges through the sample appears as a conductive response. The two processes are linked over the entire frequency range by the Kramers-Kronig relations. This is well discussed in Frohlich s book on dielectrics. 

Frohlich was the first to describe in 1954, theoretically, this type of collective electron motion. Bardeen suggested twenty years later that it may contribute to the conductivity of the organic charge transfer salt TTF-TCNQ above Tp/ and later proposed that this "Frohlich mode" gives rise to the non-linearities of the conductivity in NbSe3 observed by Monceau et al. below T. ... 

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