Phonons coherence length

The condition for observation is that the phonon coherence length is larger than the layer thickness. Low frequency acoustic modes fulfill this condition because they are an in-phase motion of a large number of atoms and are not strongly influenced by the disorder-instead reflecting the average bulk elastic properties of the materials. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

Previous studies on phonon confinement in nanocrystals did not account for possible contributions from lattice defects [100-102]. However, the parameter L in (12.3) represents the coherence length and is, therefore, a measure of the distance between dislocation, vacancies, interstitials, impurities, and other defects within the crystal lattice. The assumption that L represents the crystal size is only valid for defect-free crystals, where the surface is considered to limit the propagation of the phonons. This assumption does not hold for imperfect crystals produced by... 

The coherence length in the organic superconductors is of the order of a lattice constant (as it is for the ceramic oxide superconductors). The organic superconductors are of type II (they have two critical fields). The dimensionality is between 1 and 2 (it is 3-D for the fullerides). For organic superconductors, the isotope effect results are unclear it is not certain which phonon modes are important for the superconductivity. 

Critical exponents can also be introduced for other quantities such as the phonon gap and elastic coherence length. I he various exponents can be explained in terms of renormalization theories (see, for instance. Ref. 104). We will summarize some properties of the (one-dimensional) FK model qualitatively before focusing on more quantitative studies. Reference 105 gives a pedagogical introduction into the FK model, and Ref. 100 provides an excellent overview of the rich dynamics of the FK model. 

When the concentration of chain interruptions is sufficiently high such that the left hand side of equation 1.3 is small, then the wave function will be localised. The possible limits for the conductivity arise from the chain interruptions and/or phonon scattering. All the above factors suggest that in high-quality conducting polymers the electronic mean free path could be much larger than the structural coherence length and real metallic features could be observed. 

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