Composite Fermi liquids in the lowest Landau level
We study composite Fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling ν=1/n. We begin with the old observation that, in compressible states, the composite fermion in the lowest Landau level should be viewed as a charge-neutral particle carrying vorticity. This lead...
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| Format: | Article |
| Language: | English |
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American Physical Society
2016
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| Online Access: | http://hdl.handle.net/1721.1/105925 https://orcid.org/0000-0003-4203-4148 |
| _version_ | 1826201900976963584 |
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| author | Wang, Chong Todadri, Senthil |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Wang, Chong Todadri, Senthil |
| author_sort | Wang, Chong |
| collection | MIT |
| description | We study composite Fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling ν=1/n. We begin with the old observation that, in compressible states, the composite fermion in the lowest Landau level should be viewed as a charge-neutral particle carrying vorticity. This leads to the absence of a Chern-Simons term in the effective theory of the CFL. We argue here that instead a Berry curvature should be enclosed by the Fermi surface of composite fermions, with the total Berry phase fixed by the filling fraction ϕ[subscript B]=−2πν. We illustrate this point with the CFL of fermions at filling fractions ν=1/2q and (single and two-component) bosons at ν=1/(2q+1). The Berry phase leads to sharp consequences in the transport properties including thermal and spin Hall conductances. We emphasize that these results only rely on the LLL limit and do not require particle-hole symmetry, which is present microscopically only for fermions at ν=1/2. Nevertheless, we show that the existing LLL theory of the composite Fermi liquid for bosons at ν=1 does have an emergent particle-hole symmetry. We interpret this particle-hole symmetry as a transformation between the empty state at ν=0 and the boson integer quantum hall state at ν=2. This understanding enables us to define particle-hole conjugates of various bosonic quantum Hall states which we illustrate with the bosonic Jain and Pfaffian states. For bosons at ν=1 we construct paired non-Abelian states distinct from both the standard bosonic Pfaffian and its particle hole conjugate and show how they may arise naturally out of the neutral vortex composite Fermi liquid. The bosonic particle-hole symmetry can be realized exactly on the surface of a three-dimensional boson topological insulator. We also show that with the particle-hole and spin SU(2) rotation symmetries, there is no gapped topological phase for bosons at ν=1. Finally we comment on systems that are not strictly in the lowest Landau level limit and argue that our theory should still be applicable at low energy. |
| first_indexed | 2024-09-23T11:58:58Z |
| format | Article |
| id | mit-1721.1/105925 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:58:58Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1059252022-10-01T07:25:55Z Composite Fermi liquids in the lowest Landau level Wang, Chong Todadri, Senthil Massachusetts Institute of Technology. Department of Physics Todadri, Senthil We study composite Fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling ν=1/n. We begin with the old observation that, in compressible states, the composite fermion in the lowest Landau level should be viewed as a charge-neutral particle carrying vorticity. This leads to the absence of a Chern-Simons term in the effective theory of the CFL. We argue here that instead a Berry curvature should be enclosed by the Fermi surface of composite fermions, with the total Berry phase fixed by the filling fraction ϕ[subscript B]=−2πν. We illustrate this point with the CFL of fermions at filling fractions ν=1/2q and (single and two-component) bosons at ν=1/(2q+1). The Berry phase leads to sharp consequences in the transport properties including thermal and spin Hall conductances. We emphasize that these results only rely on the LLL limit and do not require particle-hole symmetry, which is present microscopically only for fermions at ν=1/2. Nevertheless, we show that the existing LLL theory of the composite Fermi liquid for bosons at ν=1 does have an emergent particle-hole symmetry. We interpret this particle-hole symmetry as a transformation between the empty state at ν=0 and the boson integer quantum hall state at ν=2. This understanding enables us to define particle-hole conjugates of various bosonic quantum Hall states which we illustrate with the bosonic Jain and Pfaffian states. For bosons at ν=1 we construct paired non-Abelian states distinct from both the standard bosonic Pfaffian and its particle hole conjugate and show how they may arise naturally out of the neutral vortex composite Fermi liquid. The bosonic particle-hole symmetry can be realized exactly on the surface of a three-dimensional boson topological insulator. We also show that with the particle-hole and spin SU(2) rotation symmetries, there is no gapped topological phase for bosons at ν=1. Finally we comment on systems that are not strictly in the lowest Landau level limit and argue that our theory should still be applicable at low energy. National Science Foundation (U.S.) (Grant DMR-1305741) 2016-12-21T21:01:01Z 2016-12-21T21:01:01Z 2016-12 2016-07 2016-12-05T23:00:05Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/105925 Wang, Chong, and T. Senthil. “Composite Fermi Liquids in the Lowest Landau Level.” Physical Review B 94.24 (2016): n. pag. © 2016 American Physical Society https://orcid.org/0000-0003-4203-4148 en http://dx.doi.org/10.1103/PhysRevB.94.245107 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Wang, Chong Todadri, Senthil Composite Fermi liquids in the lowest Landau level |
| title | Composite Fermi liquids in the lowest Landau level |
| title_full | Composite Fermi liquids in the lowest Landau level |
| title_fullStr | Composite Fermi liquids in the lowest Landau level |
| title_full_unstemmed | Composite Fermi liquids in the lowest Landau level |
| title_short | Composite Fermi liquids in the lowest Landau level |
| title_sort | composite fermi liquids in the lowest landau level |
| url | http://hdl.handle.net/1721.1/105925 https://orcid.org/0000-0003-4203-4148 |
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