${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect

Journal Article · 20 March 2020 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.2.013349 · OSTI ID:1605634

Balram, Ajit C.  ^[1]; Jain, J. K. ^[2]; Barkeshli, Maissam ^[3]

---

1. Univ. of Copenhagen (Denmark). The Niels Bohr Inst.; Homi Bhabha National Inst., Chennai (India)
2. Pennsylvania State Univ., University Park, PA (United States)
3. Univ. of Maryland, College Park, MD (United States)

The topological p-wave pairing of composite fermions, believed to be responsible for the 5/2 frac- tional 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 $$n\bar{n}$$111 parton wave function P_LLLΦ_nΦ$$*\atop{n}$$Φ$$3\atop{1}$$, where Φ_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 Zn superconductor of composite bosons, because the factor Φ$$3\atop{1}$$ ~ Πj_j - z_k)³, where zj = 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 Zn 2 superconducting state |Φ_n|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$$\bar{2}$$111 and 3$$\bar{3}$$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 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.

• Research Organization: Pennsylvania State Univ., University Park, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0005042
• OSTI ID: 1605634
• Alternate ID(s): OSTI ID: 1606396
• Journal Information: Physical Review Research, Vol. 2, Issue 1; ISSN 2643-1564
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English