Kohn Anomaly - Kohn Anomaly

Kohn Anomaly

In the phononic spectrum of a metal a Kohn anomaly is a discontinuity in the derivative of the dispersion relation that occurs at certain high symmetry points of the First Brillouin Zone, produced by the abrupt change in the screening of lattice vibrations by conduction electrons. Kohn anomalies arise together with Friedel oscillations when one considers the Lindhard approximation instead of the Thomas-Fermi approximation in order to find an expression for the dielectric function of a homogeneous electron gas. The expression for the real part of the dielectric function, (written in reciprocal q-space, with wave vector and frequency) obtained following Lindhard model includes, among many others, a logarithmic term which yelds a singularity for, where is the Fermi wavevector. Although this singularity is quite "small" in reciprocal space, if one takes the Fourier transform and passes in real space, the Gibbs phenomenon causes a strong oscillation of the in proximity of the singularity mentioned above. In the context of phonon dispersion relations, these oscillations appear as a vertical tangent in the plot of, the so-called Kohn anomalies.

Many different systems show this kind of anomalies, for example 2D systems like graphene, bulk metals, or many others low-dimensional systems (the reason involves the condition, which depends on the topology of the Fermi surface). However, it is important to underline that only materials showing metallic behaviour (we are dealing with approximations that need an homogeneus electron gas) are able to eventually generate a Kohn anomaly.