物理学教室 談話会(10月27日)

コロキウム・談話会 2025/10/07

講  演 者 :Thierry Martin 氏
所  属:Aix-Marseille Université (France)
タイトル:Anyon braiding, fractional charge, scaling dimension, and statistical angle in the fractional quantum Hall effect
日  時:2025年10月27日(月)15:30~17:00
場  所:理学部1号館206号室
https://scholar.google.com/citations?user=d0CBeRYAAAAJ&hl=fr

【講演者紹介】

 講師のThierry Martin教授(仏 エクス=マルセイユ大学)は1980年代から活躍されている著名な理論家です。特に1990年代初頭の量子輸送に関するロルフ・ランダウア(IBM)との共同研究が有名です。
 このセミナーでは、分数量子ホール効果における素励起「エニオン」の物理を扱います。エニオンは分数電荷を持つ素励起であり、フェルミオンともボソンとも異なる量子統計性を持っています。分数電荷は既に実験的に確認されていますが、近年になってスケーリング次元や統計角の測定が実現しました。本講演では、それら測定の理論的・実験的最先端の手法を紹介するとともに、メゾスコピック素子におけるエニオンの編み込み(braiding)を利用した新しいプロトコルを提案します。さらに階層状態や量子ドットにおけるクーロン相互作用の影響についても議論します。

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【要旨】

The fractional quantum effect is an unconventional topological state of matter with fascinating features. Its elementary excitations called “anyons” bear a fractional charge (which is specified by the filling factor of the lowest Landau level).
Anyons have a scaling dimension -aka correlation function exponent - which also correspond to this filling factor (in the absence of an electromagnetic or dissipative environment), and they have fractional statistics which is intermediate between fermions and bosons.
The fractional charge detection was proposed over three decades ago and confirmed experimentally, however only recently (in the last decade) were the scaling dimension and the so-called statistical angle measured.
I will therefore expose the present state of the art for theoretical/experimental protocols for measuring the latter two quantities and will propose a novel protocol based on anyon braiding in a mesoscopic capacitor, which allows to dissociate the measurement of the scaling dimension (which is expected to be non-universal) and the statistical angle (which is universal because it is a bulk property).
Perspectives for hierarchical states and the inclusion of Coulomb interactions in the quantum dot will be briefly mentioned.

[References]

- Anyonic Statistics Revealed by the Hong-Ou-Mandel Dip for Fractional Excitations, T. Jonckheere, J. Rech, B. Gremaud, and T. Martin, Phys. Rev. Lett. 130, 186203 (2023).
- Time-domain braiding of anyons, Science 389, (2025), M. Ruelle, E. Frigerio, E. Baudin, J.-M. Berroir, B. Placais, B. Gremaud, T. Jonckheere, T. Martin, J. Rech, A. Cavanna, U. Gennser, Y. Jin, G. Menard, and G. Feve.
- Anyon braiding on the single edge of a fractional quantum Hall state, arXiv:2503.17008, Flavio Ronetti, Noe Demazure, Jerome Rech, Thibaut Jonckheere, Benoit Gremaud, Laurent Raymond, Masayuki Hashisaka, Takeo Kato, and Thierry Martin (Phys Rev Lett, in press).
- Probing anyon statistics on a single-edge loop in the fractional quantum Hall regime, arXiv:2506.09774, Flavio Ronetti, Noe Demazure, Jerome Rech, Thibaut Jonckheere, Benoit Gremaud, Laurent Raymond, Masayuki Hashisaka, Takeo Kato, and Thierry Martin (Phys Rev B in press).

 
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