Phonons and the Isotopically Induced Mott transition - Physics

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Phonons and the Isotopically Induced Mott transition - Physics

not strictly meet this criterion as we will see in the following chapters, we will start

from this assumption and explore the limits of the parameter range over which this is

valid.

5.2 Analytic techniques for the two-site Holstein model

5.2.1 The adiabatic limit t >> h ω.

In the strong coupling limit all electrons in the conduction band are ‘dressed’ by

phonons and the hopping integral is renormalized. In his original work on small

polaron dynamics using a two-site model Holstein defined two regimes, the adiabatic

and non-adiabatic, to which different analytical approaches are applied to study this

renormalization. 28

In the adiabatic limit it is assumed that the lattice ions move much more slowly than

the valence electrons. Physically, this corresponds to an electron spending much

less time on a given site (the localization time) than required for the lattice to deform

into the polaronic configuration (the relaxation time). Because the localization time is

inversely proportional to the electronic kinetic energy (represented by the hopping

integral t within the Holstein framework) and the relaxation time is of the same order

of magnitude as the period of the lattice vibration,

in terms of the Holstein parameters: 30 hω

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