States of interacting composite fermions at Landau level fillig $\nu=2+3/8$

TL;DR

This paper investigates the possible fractional quantum Hall states at filling factor $ u=2+3/8$ by studying interacting composite fermions through variational methods and diagonalization, revealing a gapped state distinct from the Pfaffian.

Contribution

It introduces a comprehensive analysis of composite fermion interactions at $ u=2+3/8$, showing that interactions can induce a gapped fractional quantum Hall state.

Findings

Fermi sea state is favored at certain conditions.

Interactions induce a gap at the Fermi level.

The resulting state differs from the Pfaffian wave function.

Abstract

There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\nu=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\nu=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.