This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Kohn anomaly" – news ·newspapers ·books ·scholar ·JSTOR(March 2007) (Learn how and when to remove this message)

AKohn anomaly or theKohn effect is an anomaly in the dispersion relation of aphonon branch in a metal. The anomaly is named forWalter Kohn, who first proposed it in 1959.

Incondensed matter physics, a Kohn anomaly (also called the Kohn effect^[1]) is an anomaly in the dispersion relation of aphonon branch in a metal.

For a specificwavevector, thefrequency (and thus theenergy) of the associated phonon is considerably lowered, and there is a discontinuity in itsderivative. 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 forcharge density waves in solids. The wavevectors at which a Kohn anomaly is possible are the nesting vectors of theFermi surface, that is vectors that connect a lot of points of the Fermi surface (for a one-dimensional chain of atoms or a spherical Fermi surface this vector would be$2k_{\mathrm{F}}$). The electron phonon interaction causes a rigid shift of theFermi sphere and a failure of theBorn-Oppenheimer approximation since the electrons do not follow any more the ionic motion adiabatically.

In the phonon spectrum of a metal, a Kohn anomaly is a discontinuity in the derivative of the dispersion relation that is produced by the abrupt change in the screening of lattice vibrations by conduction electrons. It can occur at any point in theBrillouin Zone because$2k_{\mathrm{F}}$) is unrelated to crystal symmetry. In one dimension, it is equivalent to aPeierls instability, and it is similar to theJahn-Teller effect seen in molecular systems.

Kohn anomalies arise together withFriedel oscillations when one considers theLindhard theory instead of theThomas–Fermi approximation in order to find an expression for thedielectric function of a homogeneous electron gas. The expression for thereal part$\mathrm{Re}(\epsilon (\mathbf{q},\omega ))$ of thereciprocal space dielectric function obtained following theLindhard theory includes a logarithmic term that is singular at$\mathbf{q}=2{\mathbf{k}}_{\mathrm{F}}$, where${\mathbf{k}}_{\mathrm{F}}$ is theFermi wavevector. Although this singularity is quite small in reciprocal space, if one takes theFourier transform and passes into real space, theGibbs phenomenon causes a strong oscillation of$\mathrm{Re}(\epsilon (\mathbf{r},\omega ))$ in the proximity of the singularity mentioned above. In the context of phonondispersion relations, these oscillations appear as a verticaltangent in the plot of${\omega }^2(\mathbf{q})$, called the Kohn anomalies.

Many different systems exhibit Kohn anomalies, includinggraphene,^[2] bulk metals,^[3] and many low-dimensional systems (the reason involves the condition$\mathbf{q}=2{\mathbf{k}}_{\mathrm{F}}$, which depends on thetopology of theFermi surface). However, it is important to emphasize that only materials showingmetallic behaviour can exhibit a Kohn anomaly, since the model emerges from a homogeneous electron gas approximation.^[4][5]

The anomaly is named forWalter Kohn. They have been first proposed byWalter Kohn in 1959.^[6]

• Zero sound
• Pomeranchuk instability

• Condensed matter physics

• Articles with short description
• Short description is different from Wikidata
• Articles needing additional references from March 2007
• All articles needing additional references