Fractional topological phases in generalized Hofstadter bands with arbitrary Chern numbers

Ying Hai Wu, Jainendra K. Jain, Kai Sun

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed "topological nematic states," in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in C>1 flat bands and provides some hints on how to realize such states in experiments.

Original languageEnglish (US)
Article number041119
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number4
DOIs
StatePublished - Jan 26 2015

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Ground state
Multilayers
Statistics
Boundary conditions
Color
statistics
boundary conditions
color
ground state
Experiments
configurations
cells
interactions
Direction compound

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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Fractional topological phases in generalized Hofstadter bands with arbitrary Chern numbers. / Wu, Ying Hai; Jain, Jainendra K.; Sun, Kai.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 91, No. 4, 041119, 26.01.2015.

Research output: Contribution to journalArticle

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AB - We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed "topological nematic states," in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in C>1 flat bands and provides some hints on how to realize such states in experiments.

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