Generalized Chern-Simons theory of composite fermions in bilayer Hall systems
Abstract
We present a field theory of Jain's composite fermion model [Phys. Rev. Lett. 63, 199 (1989); Phys. Rev. B 40, 8079 (1989); 41, 7653 (1990)] as generalized to the bilayer quantum Hall systems. We define operators that create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complex version of the familiar Chern-Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in the usual Chern-Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin [Phys. Rev. B 51, 4347 (1995)] and Halperin [Helv. Phys. Acta. 56, 75 (1983)]. But unlike the normal Chern-Simons theories, we obtain all features of the first-quantized wave functions including its phase, modulus, and correct Gaussian factors at the mean-field level. The familiar Jain relations for monolayers and the Halperin wave function for bilayers come out as special cases.
- Publication:
-
Physical Review B
- Pub Date:
- September 1997
- DOI:
- 10.1103/PhysRevB.56.6788
- arXiv:
- arXiv:cond-mat/9702076
- Bibcode:
- 1997PhRvB..56.6788R
- Keywords:
-
- 73.40.Hm;
- 71.27.+a;
- 11.10.Kk;
- Strongly correlated electron systems;
- heavy fermions;
- Field theories in dimensions other than four;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- Revtex file