Second Generation of Composite Fermions

Chia‐Chen Chang

Li Chen, Sumanta Bandyopadhyay, Kun Yang +1 more

We develop recursion relations, in particle number, for all (unprojected) Jain composite fermion (CF) wave functions. These recursions generalize a similar recursion originally written down by Read for Laughlin states, in mixed first-second quantized notation. In contrast, our approach is purely second-quantized, giving rise to an algebraic, ``pure guiding center'' definition of CF states that de-emphasizes first quantized many-body wave functions. Key to the construction is a second-quantized representation of the flux attachment operator that maps any given fermion state to its CF counterpart. An algebra of generators of edge excitations is identified. In particular, in those cases where a well-studied parent Hamiltonian exists, its properties can be entirely understood in the present framework, and the identification of edge state generators can be understood as an instance of ``microscopic bosonization.'' The intimate connection of Read's original recursion with ``nonlocal order parameters'' generalizes to the present situation, and we are able to give explicit second-quantized formulas for nonlocal order parameters associated with CF states.

Arkadiusz Wójs, D. Wodziński, John J. Quinn

Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at ${\ensuremath{\nu}}_{e}=4∕11$. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at ${\ensuremath{\nu}}_{e}=4∕11$. Electron pairing occurs at ${\ensuremath{\nu}}_{e}=7∕3$ and $13∕3$, but with different pair-pair correlations. Signatures of triplets are found at higher fillings.

Gunnar M oller

Seung-Yeop Lee, Jainendra K. Jain, V. W. Scarola

Arkadiusz Wójs

We study 'second generation' of fractional quantum Hall states which contain a partially filled composite fermion (CF) Landau level (LL). We explain the role of CF-CF interaction in the incompressibility of the underlying quantum electron liquid. In particular, using exact diagonalization on a Haldane sphere, we determine two- and three-body CF correlation functions for these liquids and show that the CFs form a paired state (instead of a Laughlin liquid) when filling v = 1/3 of their second LL. At v = 1/2 we show that the CFs group into even larger clusters rather than form a Moore—Read paired state. We also address the problem of spin polarization of interacting CFs and predict transition to the partially unpolarized ground state in sufficiently narrow quantum wells and/or weak magnetic fields.