From fractional Chern insulators to a fractional quantum spin hall effect

被引：62

作者：

Goerbig, M. O. ^{[1
]}

机构：

[1] Univ Paris 11, CNRS, Phys Solides Lab, UMR 8502, F-91405 Orsay, France

来源：

EUROPEAN PHYSICAL JOURNAL B | 2012年 / 85卷 / 01期

关键词：

CONDUCTANCE; EXCITATIONS; STATES; WELLS; FLUID;

D O I：

10.1140/epjb/e2011-20857-6

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron systems in a strong magnetic field.

引用

页数：8

共 27 条

[1] Quantum spin Hall effect and topological phase transition in HgTe quantum wells [J].

Bernevig, B. Andrei ;

Hughes, Taylor L. ;

Zhang, Shou-Cheng .

SCIENCE, 2006, 314 (5806) :1757-1761

[2] Quantum spin hall effect [J].

Bernevig, BA ;

Zhang, SC .

PHYSICAL REVIEW LETTERS, 2006, 96 (10)

[3] Topological BF field theory description of topological insulators [J].

Cho, Gil Young ;

Moore, Joel E. .

ANNALS OF PHYSICS, 2011, 326 (06) :1515-1535

[4] HOMOGENEOUS AND INHOMOGENEOUS STATES OF A 2-DIMENSIONAL ELECTRON LIQUID IN A STRONG MAGNETIC-FIELD [J].

EFROS, AL .

PHYSICAL REVIEW B, 1992, 45 (19) :11354-11357

[5] Noncommutative geometry, extended W∞ algebra, and Grassmannian solitons in multicomponent quantum Hall systems -: art. no. 125314 [J].

Ezawa, ZF ;

Tsitsishvili, G ;

Hasebe, K .

PHYSICAL REVIEW B, 2003, 67 (12)

[6] Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models [J].

Fuchs, J. N. ;

Piechon, F. ;

Goerbig, M. O. ;

Montambaux, G. .

EUROPEAN PHYSICAL JOURNAL B, 2010, 77 (03) :351-362

[7] MAGNETO-ROTON THEORY OF COLLECTIVE EXCITATIONS IN THE FRACTIONAL QUANTUM HALL-EFFECT [J].

GIRVIN, SM ;

MACDONALD, AH ;

PLATZMAN, PM .

PHYSICAL REVIEW B, 1986, 33 (04) :2481-2494

[8] FRACTIONAL QUANTIZATION OF THE HALL-EFFECT - A HIERARCHY OF INCOMPRESSIBLE QUANTUM FLUID STATES [J].

HALDANE, FDM .

PHYSICAL REVIEW LETTERS, 1983, 51 (07) :605-608

[9] MODEL FOR A QUANTUM HALL-EFFECT WITHOUT LANDAU-LEVELS - CONDENSED-MATTER REALIZATION OF THE PARITY ANOMALY [J].

HALDANE, FDM .

PHYSICAL REVIEW LETTERS, 1988, 61 (18) :2015-2018

[10]

HALPERIN BI, 1983, HELV PHYS ACTA, V56, P75

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