Optical excitations in compressible and incompressible two-dimensional electron liquids

Abstract

Optically generated electron-hole pairs can probe strongly correlated electronic matter, or, by forming exciton-polaritons within an optical cavity, give rise to photonic nonlinearities. The present paper theoretically studies the properties of electron-hole pairs in a two-dimensional electron liquid in the fractional quantum Hall regime. In particular, we quantify the effective interactions between optical excitations by numerically evaluating the system's energy spectrum under the assumption of full spin and Landau level polarization. Optically most active are those pair excitations which do not modify the correlations of the electron liquid, also known as multiplicative states. In the case of spatial separation of electrons and holes, these excitations interact repulsively with each other. However, when the electron liquid is compressible, other nonmultiplicative configurations occur at lower energies. The interactions of such dark excitations strongly depend on the liquid, and can also become attractive. For the case of a single excitation, we also study the effect of Landau level mixing in the valence band which can dramatically change the effective mass of an exciton.