superconductivity of composite bosons and the fractional quantum Hall effect
Abstract
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 PLLLΦnΦ$$*\atop{n}$$Φ$$3\atop{1}$$, 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 Φ$$3\atop{1}$$ ~ Πjj - 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 2 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 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 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.
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1605634
- Alternate Identifier(s):
- OSTI ID: 1606396
- Grant/Contract Number:
- SC0005042
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 1; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; topological superconductivity; composite bosons; fractional quantum Hall effect
Citation Formats
Balram, Ajit C., Jain, J. K., and Barkeshli, Maissam. Z n superconductivity of composite bosons and the 7 / 3 fractional quantum Hall effect. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.013349.
Balram, Ajit C., Jain, J. K., & Barkeshli, Maissam. Z n superconductivity of composite bosons and the 7 / 3 fractional quantum Hall effect. United States. https://doi.org/10.1103/PhysRevResearch.2.013349
Balram, Ajit C., Jain, J. K., and Barkeshli, Maissam. Fri .
"Z n superconductivity of composite bosons and the 7 / 3 fractional quantum Hall effect". United States. https://doi.org/10.1103/PhysRevResearch.2.013349.
@article{osti_1605634,
title = {Z n superconductivity of composite bosons and the 7 / 3 fractional quantum Hall effect},
author = {Balram, Ajit C. and Jain, J. K. and Barkeshli, Maissam},
abstractNote = {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}$111 parton wave function PLLLΦnΦ$*\atop{n}$Φ$3\atop{1}$, 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 Φ$3\atop{1}$ ~ Πjj - 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 2 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 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 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.},
doi = {10.1103/PhysRevResearch.2.013349},
journal = {Physical Review Research},
number = 1,
volume = 2,
place = {United States},
year = {Fri Mar 20 00:00:00 EDT 2020},
month = {Fri Mar 20 00:00:00 EDT 2020}
}
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