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In condensed matter physics, a Kohn anomaly (also called the Kohn effect[1]) is an anomaly in the dispersion relation of a phonon branch in a metal. It is named for Walter Kohn. 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.[2] 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 ). The electron phonon interaction causes a rigid shift of the Fermi sphere and a failure of the Born-Oppenheimer approximation since the electrons do not follow any more the ionic motion adiabatically.
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 theory 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 reciprocal space dielectric function obtained following the Lindhard theory includes a logarithmic term that is singular at , where is the Fermi wavevector. Although this singularity is quite small in reciprocal space, if one takes the Fourier transform and passes into real space, the Gibbs phenomenon causes a strong oscillation of in the proximity of the singularity mentioned above. In the context of phonon dispersion relations, these oscillations appear as a vertical tangent in the plot of , called the Kohn anomalies.
Many different systems exhibit Kohn anomalies, including graphene,[3] bulk metals,[4] and many low-dimensional systems (the reason involves the condition , which depends on the topology of the Fermi surface). However, it is important to emphasize that only materials showing metallic behaviour can exhibit a Kohn anomaly, since the model emerges from a homogeneous electron gas approximation.[5][6]
^Koenig, Seymour H. (1964-09-14). "Kohn Effect in Na and other Metals". Physical Review. 135 (6A). American Physical Society (APS): A1693–A1695. Bibcode:1964PhRv..135.1693K. doi:10.1103/physrev.135.a1693. ISSN 0031-899X.
^Kohn, W. (1959). "Image of the Fermi Surface in the Vibration Spectrum of a Metal". Physical Review Letters. 2 (9): 393–394. Bibcode:1959PhRvL...2..393K. doi:10.1103/PhysRevLett.2.393.
^Piscanec, S.; Lazzeri, M.; Mauri, Francesco; Ferrari, A. C.; Robertson, J. (2004-10-28). "Kohn Anomalies and Electron-Phonon Interactions in Graphite". Physical Review Letters. 93 (18): 185503. arXiv:cond-mat/0407164. Bibcode:2004PhRvL..93r5503P. doi:10.1103/physrevlett.93.185503. ISSN 0031-9007. PMID 15525177. S2CID 46372020.
^Stewart, Derek A (2008-04-14). "Ab initio investigation of phonon dispersion and anomalies in palladium". New Journal of Physics. 10 (4): 043025. arXiv:cond-mat/0606767. Bibcode:2008NJPh...10d3025S. doi:10.1088/1367-2630/10/4/043025. ISSN 1367-2630.
^R. M. Martin, Electronic Structure, Basic Theory and Practical Methods, Cambridge University Press, 2004, ISBN 0-521-78285-6
^For experimental results, one can turn to Renker, B.; Rietschel, H.; Pintschovius, L.; Gläser, W.; Brüesch, P.; Kuse, D.; Rice, M. J. (1973-05-28). "Observation of Giant Kohn Anomaly in the One-Dimensional Conductor K2Pt(CN)4Br0.3·3H2O". Physical Review Letters. 30 (22): 1144–1147. Bibcode:1973PhRvL..30.1144R. doi:10.1103/PhysRevLett.30.1144.
a Kohnanomaly (also called the Kohn effect) is an anomaly in the dispersion relation of a phonon branch in a metal. It is named for Walter Kohn. For...
Walter Kohn (German pronunciation: [ˈvaltɐ ˈkoːn]; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist...
effective screening length is about 10 times that of metallic platinum. Kohnanomaly Pomeranchuk instability Friedel oscillations N. W. Ashcroft and N. D...
; Sato, M. (1 March 1991). "Neutron-scattering investigations of the Kohnanomaly and of the phase and amplitude charge-density-wave excitations of the...
measured anisotropy in cuprate superconductors such as LSCO and YBCO. Kohnanomaly Pomeranchuk's theorem Lindhard theory Lifshitz, E.M. and Pitaevskii,...
achievements is the derivation of the Meir-Wingreen Formula, and solving the 0.7 anomaly puzzle in quantum point contacts. Meir was educated in Tel Aviv University...
Lauper's "Girls Just Want to Have Fun" and after she calls herself an "anomaly", he nicknames her Anomalisa. The two become intimate and eventually have...
Awards Nominees". Variety. January 11, 2018. Retrieved January 12, 2018. Kohn, Eric (December 19, 2017). "2017 Critics Poll: The Best Films and Performances...
several explanations for the high mortality, including a six-year climate anomaly affecting migration of disease vectors with increased likelihood of spread...
sequestrations become infected when bacteria migrate through the Pores of Kohn or if the sequestration is incomplete. The extralobar variety accounts for...
Epidemics in Britain. Cambridge: At the University Press. p. 153. Sussman 2011. Kohn GC (2008). Encyclopedia of plague and pestilence: from ancient times to the...
increasing linearly with the NOAA global temperature anomaly and grew by a factor of 3 as the anomaly increased from 0.65 to 0.95 °C Paleolightning refers...
Records With Huge $33 Million Weekend". Forbes. Retrieved September 15, 2019. Kohn, Eric (December 11, 2019). "Jennifer Lopez Is a Gifted Actress, So Why Do...
yielded negative results, in the 1980s, John Goodkind discovered the first anomaly in a solid by using ultrasound. Inspired by his observation, in 2004 Eun-Seong...
/ New York City: John Murray / AMS Press (reprint). ISBN 0-404-14478-0. Kohn, Livia, ed. (1989). Taoist Meditation and Longevity Techniques. University...
Kluwer Academic Publishers. Bibcode:1999smad.book.....W. ISBN 1-881883-10-8. Kohn, Daniel (March 6, 2016). "The Teledesic Network: Using Low-Earth-Orbit Satellites...
prognosis. With some risk anomaly there is no difference in the life expectancy (overall survival) between patients with the anomaly detected from the diagnosis...
Robert Ford (1996). Strange Writing: Anomaly Accounts in Early Medieval China. SUNY Press. Campany 2002. Penny 2008. Kohn 2002. Sailey 1978, p. 299. Penny...
24 November 2015. Garber AK, Sawyer SM, Golden NH, Guarda AS, Katzman DK, Kohn MR, et al. (March 2016). "A systematic review of approaches to refeeding...
PMID 28993654. Halanych, Kenneth M.; Whelan, Nathan V.; Kocot, Kevin M.; Kohn, Andrea B.; Moroz, Leonid L. (2016-02-09). "Miscues misplace sponges". Proceedings...
were influenced and influences of Taoist meditation.[citation needed] Livia Kohn distinguishes three basic types of Taoist meditation: "concentrative", "insight"...
Smethwick, Chiswick and Flitwick Accordingly: Southwick, Hampshire - /ˈsʌðɪk/ Anomalies: Southwick, West Sussex is pronounced /ˈsaʊθwɪk/, like Painswick, Gloucestershire...