Comments on``Theoretical search for the nested quantum Hall effect of composite fermions" by Mandal and Jain,Phys.Rev.B 66,155302(2002); cond-mat/0210181

TL;DR

This paper critically examines Mandal and Jain's composite fermion model for the quantum Hall effect, arguing that their assumptions about flux attachment are inconsistent with electromagnetic theory and that their wave function does not solve the necessary bound-state equations.

Contribution

It provides a theoretical critique showing that the flux attachment concept in the model violates fundamental electromagnetic principles and that the wave function used is not a valid bound-state solution.

Findings

Flux attachment assumptions violate electromagnetic laws.

Wave function does not solve the bound-state equation.

The model's core premise is theoretically flawed.

Abstract

We find that a large number of parameters are used to create the correct fractions. The parameters used are, \nu, 1-\nu,\nu^*,\bar n, n, p and \bar p. Therefore, the predicted fractions need not be having the correct origin. The wave function describes a composite fermion which has the 2p (even number) of flux quanta attached to one electron. We find that it requires ``decomposite fermion", which is the electron in an orbit from which the magnetic field has been detached. This kind of detachment (attachment) of flux quanta from (to) the electron is not consistent with the electromagnetic theory of light and violates Biot and Savart's law as well as theory of relativity. If flux quanta are to be attached to the electron, we should solve the bound-state equation and determine the binding energy but bound-state has not been solved. The wave function given is not a solution of the bound-state equation. Therefore,Mandal and Jain's composite fermion (CF) model is incorrect. electron, to the electron, we should solve the bound-state equation and determine