New developments in parton theory of the fractional quantum Hall effect

In the parton construction of the FQHE [1], one divides each electron into fictitious particles called partons, places each species of partons into an IQH state, and then fuses the partons back into physical electrons. This produces candidate FQHE states that are products of IQH states. Some of the states so produced are predicted to have non-Abelian excitations. I will review recent work on the applicability of such wave functions to physically observed states at ν=5/2 [2], ν=2+6/13 [4], and ν=1/4 in wide quantum wells [4], and ν=7/3 [5]. Theory suggests that a non-Abelian "221" state may appear at ν=1/2 in bilayer and trilayer graphene [6].
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[2] A. C. Balram, S. M. Barkeshli, M.S. Rudner, Phys. Rev. B 98, 035127 (2018); Phys. Rev. B 99, 241108 (2019);
[3] A. C. Balram, S. Mukherjee, K. Park, M. Barkeshli, M. S. Rudner, J.K. Jain, Phys. Rev. Lett. 121, 186601 (2018);
[4] W. Faugno, A. C. Balram, M. Barkeshli, J. K. Jain, Phys. Rev. Lett. 123, 016802 (2019);
[5] A. C. Balram, J.K. Jain, and M. Barkeshli, Phys. Rev. Res. 2, 013349 (2020); William N. Faugno, Tongzhou Zhao, Ajit C. Balram, Thierry Jolicoeur, and Jainendra K. Jain, preprint;
[6] Y. Wu, T. Shi, J.K. Jain, Nano Letters 17, 8643 (2017).