Conductivity minimum metallic

Minimum Metallic Conductivity at the Metal - Nonmetal Transition... 

Figure 11. Schematic illustration of the two possibilities of a continuous or discontinuous metal—nonmetal transition at T = 0 K. The minimum metallic conductivity, aln,n, at the transition is also shown (from Lee and Ramakrishnan39). The conductivity at zero temperature (ordinate) and Fermi energy (abscissa) are shown. The discontinuous conductivity transition suggested by Mott is the full curve, with aTOln occuning as Ef crosses the mobility edge energy c. The dotted curve is the continuous conductivity transition predicted by the scaling theory...

Figure 14. A plot of the minimum metallic conductivity, against log nc, the critical electron density at the metal—nonmetai transition. The two straight lines correspond to the values of the constant 0.05 and 0.026 in the equation relating o,mI, and ncm (adapted from Mott44 and Fritzche46).

C104 salt did obey KR approximately. We concluded [23] that there was no qualitative change in magnetoresistance even though the (inelastic) mean free path became as low as 1/250 of a lattice parameter in the c direction. This is the experimental basis for the remarks in Section III about the possible applicability of the Boltzmann formulas even when the inelastic mean free path perpendicular to the chains is very small, and the apparent absence of a minimum metallic conductivity in the transverse directions. 

The idea of a lower limit on the scattering length leads to the concept of a minimum metallic conductivity o , = o( c)- Conduction below this value was thought to be impossible in extended states. In this model the conductivity drops discontinuously at T = 0 K because there is no conduction in the localized states below <, We shall see shortly that more recent ideas have changed this conclusion. 

We have seen in the previous section that disorder results in the localisation of charge carriers and that the conductivity will fall as a consequence of this. There is a minimum metallic conductivity, which corresponds to the electron mean free path being equal to the lattice repeat distance. The occurrence of the mobility edge means that in an amorphous metal the conductivity can switch... 

Let us estimate an order of electron conductivity value. As far as electron transport is provided through extended states of conduction band, which are not far from a mobility edge, the extreme disorder of electron scattering takes place, where between any two acts of scattering the phase coherence of electron wave turned out to be lost. In this case, according to Mott [8, 10] one may expect that pre-exponent coefficient po will correspond to the minimum metallic conductivity quantity,... 

The Fermi surface is assumed to be spherical. In the above equations, is the Fermi wave vector, / is the electron mean free path, m is the electron mass and x is the relaxation time, x = ml/Pikp. As the disorder increases, more and more states get localized and Ec and Ec move toward the centers of the respective bands. The mean free path (/) also decreases and in the limit, I = a which is the lattice distance (loffe-Regel limit). The conductivity also reaches the limit and is e 3nha), since kfl becomes approximately equal to I. Introduction of any further disorder only broadens the band and does not affect /, it alters N ( ). The minimum metallic conductivity, csm (all a values like am, , a, afO) etc. refer only to d.c. conductivities in this chapter the subscript d.c. is dropped to make the notation less cumbersome. A.c. conductivities will be referred to as cr(eo)), before the disorder localizes all the states and the conductivity drops to zero for the three dimensional problem may be approximated as 2... 

Another criterion for metallicity arises from electron localization induced by disorder proposed by Anderson. Electrons diffuse when the disorder is small, but at a critical disorder they do not diffuse (giving rise to zero conductivity). A transition from the metallic to the insulating state occurs as the disorder increases. Mott proposed that there exists a minimum metallic conductivity, a j , or maximum metallic resistivity, pmax. for which the material may still be viewed as being metallic, prior to the localization of electrons due to disorder. The Omin is given by where I is the mean free path of the electrons. Mott s... 

The minimum metallic conductivity criterion of Mott emphasizes the role of disorder. It was first realized by Anderson that electronic states originally extended can become spatially localized if the disorder is strong enough. Mott argued that in a disordered metal, the minimum possible value of the mean free path is the interatomic spacing. For stronger disorder, the picture of electron waves scattered randomly is inappropriate the electron state is localized, and one has a nonmetal. Thus, a minimum electrical conductivity, characterizes the... 

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