@article {balram_zn_2020,
title = {Z(n) superconductivity of composite bosons and the 7/3 fractional quantum {Hall} effect},
journal = {Phys. Rev. Res.},
volume = {2},
number = {1},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {mar},
abstract = {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 {\textquotedblleft}superconductivity{\textquotedblright} 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.},
doi = {10.1103/PhysRevResearch.2.013349},
author = {Balram, Ajit C. and Jain, J. K. and Barkeshli, Maissam}
}
@article {ISI:000473018000001,
title = {Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond},
journal = {Phys. Rev. B},
volume = {99},
number = {24},
year = {2019},
month = {JUN 19},
pages = {241108},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling. = k/(k + 2). Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted (\$2) over bar (k)1(k+1), and show that they lie in the same universality classes as the particle-hole-conjugate RR ({{\textquoteright}{\textquoteright}}anti-RR{{\textquoteright}{\textquoteright}}) states. Our analytical results imply that a {[}U(1)(k+1) xU(2k)(-1)]/{[}SU(k)(-2) xU(1)(-1)] coset conformal field theory describes the edge excitations of the (2) over bar (k)1(k+1) state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence (n) over bar(2) over bar (4), with n = 1, 2, 3, to describe the FQH states observed at nu= 2 + 1/2, 2 + 2/5, and 2 + 3/8.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.241108},
author = {Balram, Ajit C. and Barkeshli, Maissam and Rudner, Mark S.}
}
@article {ISI:000473540500004,
title = {Prediction of a Non-Abelian Fractional Quantum Hall State with f-Wave Pairing of Composite Fermions in Wide Quantum Wells},
journal = {Phys. Rev. Lett.},
volume = {123},
number = {1},
year = {2019},
month = {JUL 2},
pages = {016802},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We theoretically investigate the nature of the state at the quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to f-wave pairing of composite fermions. This state is topologically distinct from the familiar p-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.123.016802},
author = {Faugno, W. N. and Balram, Ajit C. and Barkeshli, Maissam and Jain, J. K.}
}
@article { ISI:000448933900006,
title = {Fractional Quantum Hall Effect at nu=2+6/13: The Parton Paradigm for the Second Landau Level},
journal = {PHYSICAL REVIEW LETTERS},
volume = {121},
number = {18},
year = {2018},
month = {NOV 1},
pages = {186601},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.121.186601},
author = {Balram, Ajit C. and Mukherjee, Sutirtha and Park, Kwon and Barkeshli, Maissam and Rudner, Mark S. and Jain, J. K.}
}
@article { ISI:000439057800004,
title = {Parton construction of a wave function in the anti-Pfaffian phase},
journal = {PHYSICAL REVIEW B},
volume = {98},
number = {3},
year = {2018},
month = {JUL 18},
pages = {035127},
issn = {2469-9950},
doi = {10.1103/PhysRevB.98.035127},
author = {Balram, Ajit C. and Barkeshli, Maissam and Rudner, Mark S.}
}