Stability and effective masses of composite-fermions in the first and second Landau Level

TL;DR

This paper investigates the stability and effective masses of composite fermions in different Landau levels, revealing conditions under which certain CF liquids can or cannot exist and estimating their effective masses.

Contribution

It introduces a measure of composite fermion stability, relates the absence of certain CF states to Landau-level mixing, and estimates CF effective masses from system size energy variations.

Findings

CF liquid at ν=2+1/2 in n=1 Landau level cannot exist under certain conditions.

A polarized CF liquid likely exists at ν=2+1/4.

Ground state energy variation suggests CF effective masses are comparable to non-interacting particles.

Abstract

We propose a measure of the stability of composite fermions (CF's) at even-denominator Landau-level filling fractions. Assuming Landau-level mixing effects are not strong, we show that the CF liquid at $\nu=2+1/2$ in the $n=1$ Landau level cannot exist and relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3 < \nu < 2+2/3$. We find that a polarized CF liquid should exist at $\nu=2+1/4$. We also show that, for CF states, the variation with system size of the ground state energy of interacting electrons follows that for non-interacting particles in zero magnetic field. We use this to estimate the CF effective masses.