Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State

TL;DR

This paper investigates the fractional quantum Hall state at filling factor 6/13, proposing it as an intermittent topological state between known states, with new wave functions and topological property predictions.

Contribution

It introduces novel wave functions for 6/13 and 5/13 states, characterizes their topological properties, and predicts their formation as intermittent states in the fractional quantum Hall regime.

Findings

State forms at ν=6/13 as an intermittent topological state.

Wave functions for 6/13 and 5/13 have high overlaps with exact ground states.

Predicted topological properties can be experimentally verified.

Abstract

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 ($\nu < 1/2$) with lower numerators, namely 4 and 5, have not yet been observed. We find that a state indeed forms at $\nu=6/13$ as an intermittent topological state between two prominent states at $\nu =1/2$ and $\nu = 2/5$ with lower numerators. Also, we predict that a state forms at $\nu=5/13$ as an intermittent to $\nu = 2/5$ and $\nu =3/8$. Our proposed wave functions for $\nu =6/13$ 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.