Topological Nematic States and Non-Abelian Lattice Dislocations

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fr...

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Main Authors: Maissam Barkeshli, Xiao-Liang Qi
Format: Article
Language:English
Published: American Physical Society 2012-08-01
Series:Physical Review X
Online Access:http://doi.org/10.1103/PhysRevX.2.031013
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author Maissam Barkeshli
Xiao-Liang Qi
author_facet Maissam Barkeshli
Xiao-Liang Qi
author_sort Maissam Barkeshli
collection DOAJ
description An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.
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spelling doaj.art-e6383abfe3ba43e1a1bfd9bd466c7dbd2022-12-21T19:54:41ZengAmerican Physical SocietyPhysical Review X2160-33082012-08-012303101310.1103/PhysRevX.2.031013Topological Nematic States and Non-Abelian Lattice DislocationsMaissam BarkeshliXiao-Liang QiAn exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.http://doi.org/10.1103/PhysRevX.2.031013
spellingShingle Maissam Barkeshli
Xiao-Liang Qi
Topological Nematic States and Non-Abelian Lattice Dislocations
Physical Review X
title Topological Nematic States and Non-Abelian Lattice Dislocations
title_full Topological Nematic States and Non-Abelian Lattice Dislocations
title_fullStr Topological Nematic States and Non-Abelian Lattice Dislocations
title_full_unstemmed Topological Nematic States and Non-Abelian Lattice Dislocations
title_short Topological Nematic States and Non-Abelian Lattice Dislocations
title_sort topological nematic states and non abelian lattice dislocations
url http://doi.org/10.1103/PhysRevX.2.031013
work_keys_str_mv AT maissambarkeshli topologicalnematicstatesandnonabelianlatticedislocations
AT xiaoliangqi topologicalnematicstatesandnonabelianlatticedislocations