Observation of filling factor 6/13 is one of the surprising fractional quantum Hall states in the second Landau level because, in contrast to the standard wisdom, the fractions (ν<1/2) with lower numerators, namely 4 and 5, have not yet been observed. We find that a state indeed forms at ν=6/13 as an intermittent topological state between two prominent states at ν=1/2 and ν=2/5 with lower numerators. Also, we predict that a state forms at ν=5/13 as an intermittent to ν=2/5 and ν=3/8. Our proposed wave functions for ν=6/13 and 5/13 have excellent overlaps with the corresponding exact ground state wave functions. The Chern-Simons coupling matrices deduced from the form of these wave functions are analyzed to predict the topological properties, which may be experimentally verified.
@article{arxiv.2409.09002,
title = {Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State},
author = {Sudipto Das and Sahana Das and Sudhansu S. Mandal},
journal= {arXiv preprint arXiv:2409.09002},
year = {2025}
}