Topological Nematic States and Non-Abelian Lattice Dislocations

By Maissam Barkeshli, Xiao-Liang Qi. 2011

145 citations recorded by the source corpus.

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall (FQH) 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 translation symmetry and topological properties of these fractional Chern insulators. When a partially filled flat band has a Chern number N, it can be mapped to an N-layer quantum Hall system. We find that lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Lattice dislocations become defects with non-trivial quantum dimension, even when the FQH 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.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cc7094f3c33cbe6773cfd0212d26d3fff9f0b69e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. J. Alicea
3. N. Lindner
4. C. Nayak
5. Matthew Fisher
6. P. Fendley
7. A. Stern
8. Masatoshi Sato

In Geometry and Topology

1. Ashvin Vishwanath
2. Matthew Fisher
3. Rahul Roy
4. M. Zaletel
5. Erez Berg
6. Parsa Bonderson

Citations in the corpus

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, background): “[84] Maissam Barkeshli and Xiao-Liang Qi, “Topological nematic states and non-abelian lattice dislocations,” Phys.”
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states (2012, background): “[44] Maissam Barkeshli and Xiao-Liang Qi, Topological Nematic States and Non-Abelian Lattice Dislocations, Phys.”
• Topological Flat Band Models and Fractional Chern Insulators (2013, background): “A particularly intriguing possibility is that lattice defects in these systems may act as worm-hole-like objects, suitably dubbed ”genons”, that change the geometry of space and obey non-Abelian exchange statistics.(41) Along with the new possibilities the topological flat band systems also pose a n”
• Fractional quantum Hall physics in topological flat bands (2013, background): “) The interplay between the lattice-scale physics and topological order in a band with C > 1 was studied in detail by Barkeshli and Qi [67].”
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface (2015, background): “[55] Maissam Barkeshli and Xiao-Liang Qi, “Topological nematic states and non-abelian lattice dislocations,” Phys.”