Kohn anomaly (original) (raw)
Die Kohn-Anomalie (nach Walter Kohn, der sie 1959 entdeckte) ist eine Anomalie der Dispersionsrelation von Phononen. Es handelt sich dabei um eine logarithmische Divergenz in der Ableitung der Dispersionsrelation. Diese Divergenz kommt von der Wechselwirkung zwischen Phononen und Elektronen und tritt immer auf der Fermifläche auf, sodass man durch Messung der Dispersion auch Informationen über die Fermifläche bekommt. Experimentell nachgewiesen wurde sie zuerst 1961 in der Gruppe von Bertram Brockhouse in .
| Property | Value |
|---|---|
| dbo:abstract | Die Kohn-Anomalie (nach Walter Kohn, der sie 1959 entdeckte) ist eine Anomalie der Dispersionsrelation von Phononen. Es handelt sich dabei um eine logarithmische Divergenz in der Ableitung der Dispersionsrelation. Diese Divergenz kommt von der Wechselwirkung zwischen Phononen und Elektronen und tritt immer auf der Fermifläche auf, sodass man durch Messung der Dispersion auch Informationen über die Fermifläche bekommt. Die Kohn-Anomalie ist u. a. verantwortlich für den Peierls-Übergang in eindimensionalen Molekülketten wie Polyethin und den Jahn-Teller-Übergang in dreidimensionalen Kristallen. Sie kann eine spontane Brechung der Gittersymmetrie aufgrund elektronischer Energieminimierung bewirken. Experimentell nachgewiesen wurde sie zuerst 1961 in der Gruppe von Bertram Brockhouse in . (de) In the field of physics concerning condensed matter, a Kohn anomaly (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 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 ). 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, bulk metals, 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. (en) コーン異常とは、金属中のフォノン分散関係の異常のこと。フォノンの周波数、つまりエネルギーがある波数ベクトルで非常に低くなり、微分係数が不連続になる。1959年にウォルター・コーンによって提案された。極端な場合（低次元材料で起こり得る）、このフォノンのエネルギーは0となり、格子の静的な歪みが現れる。これは固体の電荷密度波の原因の1つである。コーン異常が起こり得る波数ベクトルはフェルミ面のネスティングベクトルであり、フェルミ面の数多くの点をつなげるベクトルである（1次元の原子鎖におけるこのベクトルはである）。 金属のフォノンスペクトルにおいて、コーン異常は分散関係の微分係数における不連続点である。これは第一ブリルアンゾーンの対称性の高い点で起こり、伝導電子による格子振動の遮蔽の急激な変化によって生じる。均一な電子ガスの誘電関数を求めるためにトーマス・フェルミ近似ではなくを考えたとき、コーン異常はフリーデル振動と共に生じる。リンドハード模型から得られた逆格子空間での誘電関数の実部 は対数項を含んでおり、で特異性をもつ。ここではフェルミ波数である。この特異性は逆格子空間では非常に小さいにもかかわらず、フーリエ変換をして実空間に移った場合、上述の特異点の近くでギブズ現象によりの強い振動が起こる。フォノン分散関係において、これらの振動はのプロットにおける垂直接戦として現れ、コーン異常と呼ばれる。 グラフェン、バルク金属、多くのなど多くの系でコーン異常は見られる（理由は条件を含み、フェルミ面のトポロジーに依存する）。しかしコーン異常を示すのは、均一電子ガス近似を扱う金属的な振る舞いを示す物質だけである。 (ja) Uma anomalia de Kohn é uma anomalia na relação de dispersão de um ramo de fônon em um metal. Para um vetor de onda específico, a frequência (e, portanto, a energia) do fônon associado é consideravelmente reduzida e há uma descontinuidade em sua derivada. Eles foram propostos pela primeira vez por Walter Kohn em 1959. Esses estados exóticos podem oferecer pistas sobre por que alguns materiais têm as propriedades eletrônicas que possuem. Muitos sistemas diferentes exibem anomalias de Kohn, incluindo grafeno, metais a granel e muitos sistemas de baixa dimensão (a razão envolve a condição , depende da topologia da superfície de Fermi). No entanto, é importante enfatizar que apenas materiais que mostram comportamento metálico podem exibir uma anomalia de Kohn, pois estamos lidando com aproximações que precisam de um gás de elétrons homogêneo. (pt) |
| dbo:wikiPageID | 9585894 (xsd:integer) |
| dbo:wikiPageLength | 5482 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1109347026 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Derivative dbr:Reciprocal_lattice dbr:Lindhard_theory dbr:Energy dbr:Frequency dbr:Condensed_matter_physics dbr:Friedel_oscillations dbr:Physics dbr:Tangent dbc:Condensed_matter_physics dbr:Topology dbr:Walter_Kohn dbr:Dispersion_relation dbr:Fourier_transform dbr:Brillouin_zone dbr:Graphene dbr:Born-Oppenheimer_approximation dbr:Fermi_sphere dbr:Phonon dbr:Pomeranchuk_instability dbr:Fermi_energy dbr:Fermi_surface dbr:Metal dbr:Real_part dbr:Spin_density_wave dbr:Zero_sound dbr:Gibbs_phenomenon dbr:Thomas–Fermi_approximation dbr:Dielectric_function dbr:Wavevector |
| dbp:wikiPageUsesTemplate | dbt:Refimprove |
| dcterms:subject | dbc:Condensed_matter_physics |
| rdfs:comment | Die Kohn-Anomalie (nach Walter Kohn, der sie 1959 entdeckte) ist eine Anomalie der Dispersionsrelation von Phononen. Es handelt sich dabei um eine logarithmische Divergenz in der Ableitung der Dispersionsrelation. Diese Divergenz kommt von der Wechselwirkung zwischen Phononen und Elektronen und tritt immer auf der Fermifläche auf, sodass man durch Messung der Dispersion auch Informationen über die Fermifläche bekommt. Experimentell nachgewiesen wurde sie zuerst 1961 in der Gruppe von Bertram Brockhouse in . (de) In the field of physics concerning condensed matter, a Kohn anomaly (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 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 (en) コーン異常とは、金属中のフォノン分散関係の異常のこと。フォノンの周波数、つまりエネルギーがある波数ベクトルで非常に低くなり、微分係数が不連続になる。1959年にウォルター・コーンによって提案された。極端な場合（低次元材料で起こり得る）、このフォノンのエネルギーは0となり、格子の静的な歪みが現れる。これは固体の電荷密度波の原因の1つである。コーン異常が起こり得る波数ベクトルはフェルミ面のネスティングベクトルであり、フェルミ面の数多くの点をつなげるベクトルである（1次元の原子鎖におけるこのベクトルはである）。 グラフェン、バルク金属、多くのなど多くの系でコーン異常は見られる（理由は条件を含み、フェルミ面のトポロジーに依存する）。しかしコーン異常を示すのは、均一電子ガス近似を扱う金属的な振る舞いを示す物質だけである。 (ja) Uma anomalia de Kohn é uma anomalia na relação de dispersão de um ramo de fônon em um metal. Para um vetor de onda específico, a frequência (e, portanto, a energia) do fônon associado é consideravelmente reduzida e há uma descontinuidade em sua derivada. Eles foram propostos pela primeira vez por Walter Kohn em 1959. Esses estados exóticos podem oferecer pistas sobre por que alguns materiais têm as propriedades eletrônicas que possuem. Muitos sistemas diferentes exibem anomalias de Kohn, incluindo grafeno, metais a granel e muitos sistemas de baixa dimensão (a razão envolve a condição , depende da topologia da superfície de Fermi). No entanto, é importante enfatizar que apenas materiais que mostram comportamento metálico podem exibir uma anomalia de Kohn, pois estamos lidando com aproximaç (pt) |
| rdfs:label | Kohn-Anomalie (de) Kohn anomaly (en) コーン異常 (ja) Anomalia de Kohn (pt) |
| owl:sameAs | freebase:Kohn anomaly wikidata:Kohn anomaly dbpedia-de:Kohn anomaly dbpedia-ja:Kohn anomaly dbpedia-pt:Kohn anomaly https://global.dbpedia.org/id/2GFfW |
| prov:wasDerivedFrom | wikipedia-en:Kohn_anomaly?oldid=1109347026&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Kohn_anomaly |
| is dbo:knownFor of | dbr:Walter_Kohn |
| is dbo:wikiPageRedirects of | dbr:Kohn_effect |
| is dbo:wikiPageWikiLink of | dbr:Index_of_physics_articles_(K) dbr:Lindhard_theory dbr:Walter_Kohn dbr:Born–Oppenheimer_approximation dbr:Pomeranchuk_instability dbr:Kohn_effect |
| is dbp:knownFor of | dbr:Walter_Kohn |
| is foaf:primaryTopic of | wikipedia-en:Kohn_anomaly |