Multi-component wave functions and the fractional quantum Hall effect

Nicolas Regnault

Laboratoire Pierre Aigrain; France

Multi-component quantum Hall systems, i.e. 2D electrons with an internal symmetry in a strong perpendicular magnetic field, may be generically described in terms of an "iso-spin". The issue has been addressed both for the "real" electron spin or the layer index in the case of bilayer systems. Recently, new physical systems such as graphene, have motivated a deeper look at internal degrees of freedom, namely because graphene reveals an isospin structure due to a two-fold valley degeneracy in addition to the physical spin.
We present the different strategies which have been developed to study quantum Hall systems with internal degrees of freedom. We mainly focus on the generalized SU(K) Halperin wave functions, which are a straightforward generalization of the Laughlin state to a system with K electron components [1]. Within the picture of the plasma analogy, we show how larger symmetry groups open new perspectives in fractional quantum Hall physics [2]. We finally comment on the relation between these multi-component wave functions and the non-Abelian states in the usual (one-component) fractional quantum Hall effect.
[1] M.O. Goerbig and N. Regnault, Phys. Rev. B 75, 241405(R) (2007).
[2] R. de Gail, N. Regnault, and M.O. Goerbig, arXiv:0710.5905; to be published in Phys. Rev. B.