Interaction with phonons and polaron formation

The phonons (lattice vibrations) in a solid or liquid conductor have the following effects on mobile electrons or holes. 

The behaviour of polarons is of importance for the oxides and similar materials to be discussed in this book, and we summarize some of their properties here, as applied chiefly to transitional-metal oxides. (For more detailed discussions see Mott and Davis (1979, Chap. 3), Austin and Mott (1969a, b), Appel (1968), Emin (1973, 1975) and Mott (1973b). 

In ionic crystals a polaron is the region round an electron in the conduction band in which the material is polarized by the electron, as first proposed by Landau (1933). Round the electron, the field with which it interacts has a potential-energy function 

This can be seen from elementary considerations. The distortion of the surrounding medium that leads to the intermediate state with energy WH can be described by simple harmonic motion, with a parameter x for the displacement, a potential energy px2 and a wave function of the form r=const xexp(—ax2). The probability P 2 of a configuration with potential energy WH is thus 

A very similar situation is presented by the dynamic Jahn-Teller effect, in which a trapped electron that has distorted its surroundings hops between two configurations with a frequency given by (6) for a proof see Sturge (1967). 

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