Particle-hole mirror symmetries around the half-filled shell: Quantum numbers and algebraic structure of composite fermions
- University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- University of California, Berkeley, CA (United States); KLA-Tencor, Fremont, CA (United States)
Composite fermions (CFs) of the fractional quantum Hall effect (FQHE) are described as spherical products of electron and vortex spinors, built from underlying πΏ=1/2 ladder operators aligned so that the spinor angular momenta, πΏπ and πΏπ£, are maximal. We identify the CF's quantum numbers as the angular momentum πΏ in (πΏπβ’πΏπ£)β’πΏ, its magnetic projection ππΏ, the electron number π [πΏπ£=(πβ1)/2], and magnetic π spin, ππ = πΏπβπΏπ£. Translationally invariant FQHE states are formed by fully filling π subshells with their respective CFs, in order of ascending πΏ for fixed πΏπ and πΏπ£, beginning with the lowest allowed value, πΏ=|β’ππ|. CF subshells are contained entirely within the first Landau level (FLL). Alternatively, we provide an equivalent hierarchical wave function in which the underlying objects are vortices with πΏπ£= $$\frac{p}{2}$$, correlated. Here, we show that CFs can be written as a valence operator carrying the angular momentum quantum numbers πΏ, ππ, ππΏ acting on a scalar half-filled intrinsic state.
- Research Organization:
- University of California, Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- Grant/Contract Number:
- SC0004658; AC02-05CH11231
- OSTI ID:
- 2907336
- Alternate ID(s):
- OSTI ID: 1471799
- Journal Information:
- Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 98; ISSN 2469-9969; ISSN 2469-9950
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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