Higher energy modes of Fractional quantum Hall Effect

TL;DR

This paper calculates the energy spectra of various filling fractions in the Jain series of the fractional quantum Hall effect, revealing multiple roton minima in higher energy modes using composite fermion theory.

Contribution

It introduces detailed calculations of higher energy modes and their roton minima in the fractional quantum Hall effect for the Jain series.

Findings

Multiple roton minima observed in higher energy modes.

Low and high energy modes share similar nature.

Energy spectra computed for nearly all Jain series filling fractions.

Abstract

We have calculated the energy spectra for almost all the filling fractions in the Jain series low energy fundamental mode as well as higher energy modes using composite fermion theory. The nature of the low energy mode and higher energy mode is nearly identical to the roton mode. We have observed that, these series of filling fractions $\nu=\frac{n}{2pn+1}$ possess $n$ number of roton minima in their higher energy mode.