Applications of gauge theories to lowdimensional electron systems
Project/Area Number  10640265 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
素粒子・核・宇宙線

Research Institution  KYOTO UNIVERSITYKYOTO UNIVERSITY 
Principal Investigator 
SHIZUYA Kenichi Kyoto University, Yukawa Inst. for Theor. Phys., Professor, 基礎物理学研究所, 教授 (50154216)

Project Fiscal Year 
1998 – 2001

Project Status 
Completed(Fiscal Year 2001)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 2001 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 2000 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Gauge Theory / Quantum Hall Effect / Localization / Edge Current / Bosonization / DoubleLayer Systems / Collective Excitations / ChernSimons Theory / ゲージ理論 / 整数量子ホール効果 / 分数量子ホール効果 / 量子ホール効果の消失 / 局在 / 端電流 / 二層系 / ボゾン化 / 集団励起 / コヒーレンス / 複合フェルミオン / 量子ホール効果 / 輸送現象 / 対称性 
Research Abstract 
It is now widely accepted that gauge fields play an important role in condensedmatter physics as well as in particle physics. In particular, as seen from the observation of Skyrmion excitations in quantum Hall systems, lowdimensional electron systems offer a good and practical place to test and apply various ideas of gauge theories. Under a GrantinAid over the past four years, we have thus studied some problems pertaining to the foundation of the quantum Hall effect by use of gauge theories. 1. Hallcurrent distribution : The current distribution in a Hall sample is a subject of basic importance. We had earlier pointed out that a considerable portion of the Hall current would flow along the sample edges as a consequence of expulsion out of the localizationdominated sample interior. We carried out a numerical experiment to verify this picture of the bulkedge Hall current. 2. Breakdown of the quantum Hall effect : A mechanism for the breakdown of the quantum Hall effect, suggested from the above numerical experiment, was examined by a further numerical analysis. It was pointed out that the observed breakdown phenomena may be explained by an intraLandaulevel process, competition between disorder and the Hall field. 3. Fractional quantum Hall effect (FQHE) : A new approach to the effective theory of the FQHE was developed, that makes use of projection to Landau levels and bosonization and that relies on the incompressible nature of the quantum Hall states without referring to the standard compositeboson or composite fermion picture. In particular, for doublelayer systems we succeeded in constructing an effective gauge theory that properly incorporates the collectiveexcitation spectrum, known from a general magnetoroton theory but inaccessible by the conventional ChernSimons theories. 4.上述の研究についてはオタワとプラハで開催された2次元電子系の国際会議にてその成果を報告した。

Report
(6results)
Research Output
(19results)