Kohn anomaly in phonon driven superconductors

Anomalies often occur in the physical world. Sometimes quite unexpectedly anomalies may give rise to new insight to an unrecognized phenomenon. In this paper we shall discuss about Kohn anomaly in a conventional phonon-driven superconductor by using a microscopic approach. Recently Aynajian et al.'s experiment showed a striking feature; the energy of phonon at a particular wave-vector is almost exactly equal to twice the energy of the superconducting gap. Although the phonon mechanism of superconductivity is well known for many conventional superconductors, as has been noted by Scalapino, the new experimental results reveal a genuine puzzle. In our recent work we have presented a detailed theoretical analysis with the help of microscopic calculations to unravel this mystery. We probe this aspect of phonon behaviour from the properties of electronic polarizability function in the superconducting phase of a Fermi liquid metal, leading to the appearance of a Kohn singularity. We show the crossover to the standard Kohn anomaly of the normal phase for temperatures above the transition temperature. Our analysis provides a nearly complete explanation of this new experimentally discovered phenomenon. This report is a shorter version of our recent work in JPCM.