Collective excitations of composite fermions across multiple levels

The fractional quantum Hall state is a quintessential system for the study of collective quantum behaviour. In such a system, the collective behaviour results in the creation of so-called composite fermions, quasi-particles formed by electrons attached to magnetic flux quanta. Recently, a new collective mode was unexpectedly observed in Raman scattering experiments on such a system as it was found to split off from the familiar fundamental long-wavelength mode on increase of the wave vector. Here, we present results from extensive theoretical calculations that make a compelling case that this mode corresponds to an excitation of a composite fermion across two levelseffective kinetic energy levels resembling Landau levels for such particles. In addition to explaining why this excitation merges with the fundamental mode in the long-wavelength limit, our theory also provides a good quantitative account of the amount of splitting, and makes several experimentally verifiable predictions.