Photoluminescence from fractional quantum Hall systems: Role of separation between electron and hole layers

Abstract

The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied as a function of the separation d between the electron and valence hole layers. The abrupt change in the response of the 2DEG to the optically injected hole at d of the order of the magnetic length λ results in a complete reconstruction of the PL spectrum. At d < λ, the hole binds one or two electrons to form neutral (X) or charged (X − ) excitons, and the PL spectrum probes the lifetimes and binding energies of these states rather than the original correlations of the 2DEG. At d > 2λ, depending on the filling factor ν, the hole either decouples from the 2DEG to form an "uncorrelated" state h or binds one or two Laughlin quasielectrons (QE) to form fractionally charged excitons hQE or hQE2. The strict optical selection rules for bound states are formulated, and the only optically active ones turn out to be h, hQE* (an excited state of the dark hQE), and hQE2. The "anyon exciton" hQE3 suggested in earlier studies is neither stable nor radiative at any value of d. The critical dependence of the stability of different states on the presence of QE's in the 2DEG explains the observed anomalies in the PL spectrum at ν =

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

“…Exciton properties can be calculated from the configuration-interaction approach to interacting electrons [304,305], particularly useful in studies of nanostructures, e.g., quantum dots [306][307][308][309][310][311][312][313][314][315][316][317][318][319][320][321][322] or electron gas in quantum wells in strong magnetic fields [323,324]. This approach has only recently been utilized to study excitons in reciprocal space [230,281].…”

Photoluminescence fine structures in the fractional quantum Hall effect regime

“…To understand the above observations, following earlier work [18,23,26,33,34], we study recombination spectra of an exciton interacting with an increasing number of electrons N e on the Haldane sphere [35]. An infinite two-dimensional plane is mapped onto the Haldane sphere, at the center of which there is a magnetic monopole of strength 2S.…”

“…[16] However, the understanding of the PL in the FQHE regime, especially the PL in the σ + polarization, has been limited until now despite extensive theoretical investigations [18,[23][24][25][26][27]. For example, the effect of the electron-hole Coulomb interaction on the spin configuration of the electrons-hole system in the FQHE state has not been fully understood.…”