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Z(n) superconductivity of composite bosons and the 7/3 fractional quantum Hall effect

TitleZ(n) superconductivity of composite bosons and the 7/3 fractional quantum Hall effect
Publication TypeJournal Article
Year of Publication2020
AuthorsA. C. Balram, J.. K. Jain, and M. Barkeshli
JournalPhys. Rev. Res.
Date Publishedmar

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 n (n) over bar 111 parton wave function P-LLL Phi(n)Phi(n)*Phi(3)(1), where Phi(n) is the wave function of the integer quantum Hall state with n filled Landau levels and P-LLL is the lowest-Landau-level projection operator. It represents a Z(n) superconductor of composite bosons, because the factor Phi(3)(1) similar to Pi(j{\textless}k) (z(j) - z(k))(3), where z(j) = x(j) - iy(j) is the coordinate of the jth electron, binds three vortices to electrons to convert them into composite bosons, which then condense into the Z(n) superconducting state vertical bar Phi(n)vertical bar(2). From a field theoretical perspective, this state can be understood by starting with the usual Laughlin theory and gauging a Z(n) subgroup of the U(1) charge conservation symmetry. We find from detailed quantitative calculations that the 2{\textless}(2)over bar{\textgreater}111 and 3 (3) over bar 111 states are at least as plausible as the Laughlin wave function for the exact Coulomb ground state at filling nu = 7/3, suggesting that this physics is possibly relevant for the 7/3 FQHE. The Z(n) 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 Z(n) superconductivity.