TOPOLOGICAL FLAT BAND MODELS AND FRACTIONAL CHERN INSULATORS

被引:405
作者
Bergholtz, Emil J. [1 ]
Liu, Zhao [2 ]
机构
[1] Free Univ Berlin, Inst Theoret Phys, Dahlem Ctr Complex Quantum Syst, D-14195 Berlin, Germany
[2] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China
来源
INTERNATIONAL JOURNAL OF MODERN PHYSICS B | 2013年 / 27卷 / 24期
基金
中国博士后科学基金;
关键词
Fractional Chern insulators; flat bands; topological insulators; topological order; anyons; fractional quantum Hall effect; QUANTIZED HALL CONDUCTANCE; INCOMPRESSIBLE QUANTUM FLUID; WAVE-FUNCTIONS; WANNIER FUNCTIONS; STATES; TRANSITION; ELECTRONS; HIERARCHY; FERMIONS;
D O I
10.1142/S021797921330017X
中图分类号
O59 [应用物理学];
学科分类号
摘要
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with nonzero Chern number, C. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with nontrivial topology, C not equal 0, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with vertical bar C vertical bar > 1. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.
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页数:43
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