Optical probing of electronic fractional quantum Hall states

Abstract

We report on the observation of a fine structure in the photoluminescence emission of high-mobility GaAs/ AlGaAs single heterojunctions in the fractional quantum Hall regime. A splitting of the emission band into three lines is found both at filling factor v = 2 l3 and in the region 2/5 > v > 1 /3. The dependencies on filling factor, electron density, and temperature show that the fine structure arises from the recombination of fraction ally charged elementary excitations of the two-dimensional electron liquid and an itinerant valence-band hole. These quasiparticle excitations (anyon excitons) exhibit a dispersion relation with an absolute minimum at large momentum, leading to a characteristic, broad emission band at the low-energy side of the photolumines cence spectrum around v= 1l 3.

Optical probing of the metal-to-insulator transition in a two-dimensional high-mobility electron gas

“…Usually asymmetric QW do not exhibit a clear kink at ν = 2 (it has been argued that the hidden symmetry can't hold in this case) but this is not in contrast with our finding, since as demonstrated by Hayne et al [16], also for an asymmetric QW it's possible to observe this strong shift as well as the quadratic behavior if the band has been flattened by photo-irradiation or when the width of the QW is not too wide. Recently Blokland et al [10] studied the photoluminescence emission in the fractional quantum Hall regime, analyzing the fine structure arising from the recombination of fractional charged elementary excitations on the 2DEG and the itinerant valence band holes. The experiments reveals a splitting of the emission band in three lines at ν = 2/3 and in the region 2/5 > ν > 1/3, with a lowest-energy emission between ν = 2/5 and ν = 1/3 from magneto-roton assisted transitions from the ground state of the photo-excited fractional quantum Hall system.…”

“…This transition to the insulating state, called also twodimensional metal-insulator transition, has been studied by electrical transport, and has been found that for low mobility samples the transition occurs beyond the ν = 1 quantum Hall state (being ν = nh/(eB) the filling factor) while in high mobility GaAs-AlGaAs samples the transition takes place beyond the ν = 1/3 state or the ν = 1/5 state [8]. This liquid-to-insulator transition has been successively studied in details by electrical transport, in low mobility samples like InGaAs/InP and Ge/SiGe and in GaAs-AlGaAs high mobility structures [8] and recently in graphene [9], while the high field regime has been studied optically by PL concerning the emission energy and line-shape [6,10]. The nature of the insulating state is still an open question, since the Anderson localization (due to disorder) and the Mott localization (driven by the strong correlation between the interacting electrons) are the two candidates for the explanation of the phenomenon [11,12].…”