Theory of anyon excitons: Relation to excitons of ν=1/3 and ν=2/3 incompressible liquids

Abstract

Elementary excitations of incompressible quantum liquids (IQL’s) are anyons, i.e., quasiparticles carrying fractional charges and obeying fractional statistics. To find out how the properties of these exotic quasiparticles manifest themselves in the optical spectra, we have developed the anyon-exciton model (AEM) and compared the results with the finite-size data for excitons of ν=1/3 and ν=2/3 IQL’s. The model considers an exciton as a neutral composite consisting of three quasielectrons and a single hole. The AEM works well when the separation between electron and hole confinement planes, h, obeys the condition h≳2l, where l is the magnetic length. In the framework of the AEM an exciton possesses momentum k and two internal quantum numbers, one of which can be chosen as the angular momentum L of the k=0 state. Charge fractionalization manifests itself in striking differences between the properties of anyon excitons and ordinary magnetoexcitons. The existence of the internal degrees of freedom results in the multiple-branch energy spectrum, craterlike electron density shape, and 120° density correlations for k=0 excitons, and the splitting of the electron shell into bunches for k≠0 excitons. For h≳2l the bottom states obey the superselection rule L=3m, where m≥2 are integers, and all of them are hard-core states. For h≊2l there is one-to-one correspondence between the low-energy spectra found for the AEM and the many-electron exciton spectra of the ν=2/3 IQL, whereas some states are absent from the many-electron spectra of the ν=1/3 IQL. We argue that this striking difference in the spectra originates from the different populational statistics of the quasielectrons of charge conjugate IQL’s and show that the proper account of the statistical requirements eliminates excessive states from the spectrum. Apparently, this phenomenon is the first manifestation of the exclusion statistics in the anyon bound states.