Theory of coherence length and phonon softening inA−15compounds

Coherence lengths and phonon softening in $A-15$ compounds are investigated on the basis of existing one-dimensional models and a recent three-dimensional tight-binding model. Results are found to depend sensitively on the band structure near the Fermi surface, and the tight-binding model is found to give a very short coherence length ($\frac{{\xi }_0}{a}\ll \frac{E_F}{T_c}$), in agreement with the extensive softening of finite-wave-vector phonons seen by neutron scattering. General remarks on phonon softening in models with three-dimensional peaked density of states and on some consequences of the short coherence length are made.