### Abstract

This paper reports on our study of the edge of the 25 fractional quantum Hall state, which is more complicated than the edge of the 13 state because of the presence of edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a nonperturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N _{1},N _{2}] sector, where N _{1} and N _{2} are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N _{1}+1,N _{2}] or [N _{1},N _{2}+1] sectors; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N _{1}+1+k,N _{2}-k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed comparison with the two-boson model of the 25 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and nonuniversal, their sum is consistent with an effective two-boson description of the 25 edge.

Original language | English (US) |
---|---|

Article number | 245104 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 84 |

Issue number | 24 |

DOIs | |

State | Published - Dec 9 2011 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*84*(24), [245104]. https://doi.org/10.1103/PhysRevB.84.245104

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 84, no. 24, 245104. https://doi.org/10.1103/PhysRevB.84.245104

**Microscopic study of the 25 fractional quantum Hall edge.** / Sreejith, G. J.; Jolad, Shivakumar; Sen, Diptiman; Jain, Jainendra K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Microscopic study of the 25 fractional quantum Hall edge

AU - Sreejith, G. J.

AU - Jolad, Shivakumar

AU - Sen, Diptiman

AU - Jain, Jainendra K.

PY - 2011/12/9

Y1 - 2011/12/9

N2 - This paper reports on our study of the edge of the 25 fractional quantum Hall state, which is more complicated than the edge of the 13 state because of the presence of edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a nonperturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N 1,N 2] sector, where N 1 and N 2 are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N 1+1,N 2] or [N 1,N 2+1] sectors; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N 1+1+k,N 2-k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed comparison with the two-boson model of the 25 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and nonuniversal, their sum is consistent with an effective two-boson description of the 25 edge.

AB - This paper reports on our study of the edge of the 25 fractional quantum Hall state, which is more complicated than the edge of the 13 state because of the presence of edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a nonperturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N 1,N 2] sector, where N 1 and N 2 are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N 1+1,N 2] or [N 1,N 2+1] sectors; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N 1+1+k,N 2-k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed comparison with the two-boson model of the 25 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and nonuniversal, their sum is consistent with an effective two-boson description of the 25 edge.

UR - http://www.scopus.com/inward/record.url?scp=84855410461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855410461&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.84.245104

DO - 10.1103/PhysRevB.84.245104

M3 - Article

AN - SCOPUS:84855410461

VL - 84

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 24

M1 - 245104

ER -