Zn superconductivity of composite bosons and the 7/3 fractional quantum Hall effect

The topological p-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. Motivated by the parton theory of the FQHE, we consider the possibility of a new kind of emergent "superconductivity"in the 1/3 FQHE, which involves condensation of clusters of n composite bosons. From a microscopic perspective, the state is described by the nn¯111 parton wave function PLLLφnφn∗φ13, where φn is the wave function of the integer quantum Hall state with n filled Landau levels and PLLL is the lowest-Landau-level projection operator. It represents a Zn superconductor of composite bosons, because the factor φ13∼<k(zj-zk)3, where zj=xj-iyj is the coordinate of the jth electron, binds three vortices to electrons to convert them into composite bosons, which then condense into the Zn superconducting state |φn|2. From a field theoretical perspective, this state can be understood by starting with the usual Laughlin theory and gauging a Zn subgroup of the U(1) charge conservation symmetry. We find from detailed quantitative calculations that the 22¯111 and 33¯111 states are at least as plausible as the Laughlin wave function for the exact Coulomb ground state at filling ν=7/3, suggesting that this physics is possibly relevant for the 7/3 FQHE. The Zn order leads to several observable consequences, including quasiparticles with fractionally quantized charges of magnitude e/(3n) and the existence of multiple neutral collective modes. It is interesting that the FQHE may be a promising venue for the realization of exotic Zn superconductivity.