A Kohn anomaly is an anomaly in the dispersion relation of a phonon branch in a metal. For a specific wavevector, the frequency—and thus the energy—of the associated phonon is considerably lowered, and there is a discontinuity in its derivative. They have been first proposed by Walter Kohn in 1959. In extreme cases (that can happen in low-dimensional materials), the energy of this phonon is zero, meaning that a static distortion of the lattice appears. This is one explanation for charge density waves in solids. The wavevectors at which a Kohn anomaly is possible are the nesting vectors of the Fermi surface, that is vectors that connect a lot of points of the Fermi surface (for a one-dimensional chain of atoms this vector would be
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
Many different systems exhibit Kohn anomalies, including graphene, bulk metals, and many low-dimensional systems (the reason involves the condition