Calculation of Binding Energies for Fractional Quantum Hall States with Even Denominators

TL;DR

This paper calculates the binding energies of fractional quantum Hall states with even denominators using second-order perturbation theory, providing insights into experimental resistivity minima and the nature of these non-standard states.

Contribution

It introduces a method to compute binding energies for non-standard fractional quantum Hall states with even denominators, expanding understanding beyond composite fermion models.

Findings

Binding energies are non-zero for specific filling factors like 5/8 and 7/10.

Binding energies are zero for many other fractional states such as 1/2 and 1/4.

Higher order calculations confirm the results of second-order perturbation theory.

Abstract

Fractional quantum Hall states with even denominators have the following specific properties: states with filling factors nu=5/8, 7/10, 3/8, 3/10, and so on have respective local minima in the experimental curve of diagonal resistivity Rxx versus magnetic field strength. These states are not standard composite fermion states and are described in the expanded framework. For that reason, the binding energies of these states are not obtained. Therefore, it is meaningful to calculate those binding energies using various means. We calculate the binding energies of electron pairs in nearest neighbor orbitals or nearest neighbor hole pairs using the second-order perturbation method for the Coulomb interactions among many electrons. The calculated binding energies per electron are (1/10)Z2 for nu=5/8, (2/35)Z2 for nu=7/10, (1/6)Z2 for nu=3/8 and (2/15)Z2 for nu=3/10 and so on, but they are zero for nu=1/2, nu=1/4, nu=3/4, nu=1/6, nu=5/6, nu=1/8, nu=7/8, nu=1/10, nu=9/10, nu=1/12 and nu=11/12. The higher order calculations also show the same behavior as in the second order. These results further elucidate some aspects of experimental data.