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2009 TWO DIMENSIONAL ELECTRON GASSpin splitting enhancement of fully populated Landau levelsThe effect known as “g-factor enhancement” is the prominentmanifestation of electron-electron interactions in thestudy of a two-dimensional electron gas (2DEG) in theregime of the integer quantum Hall effect. This effect isroutinely apparent in magneto-transport experiments. Theyshow that thermal activation of charged carriers across theFermi energy located in between spin split Landau levels(2DEG at odd filling factors) is ruled by the gap which cansignificantly surpass the so called bare gap expected fromsingle particle band structure models. As far, the effect of g-factor enhancement (at odd filling factors) has been mostlyapparent in experiments which probed the vicinity of theFermi level. As illustrated in figure. 35, the motivation ofour work was to check whether g-factor is also enhancedfor spin split Landau levels located deep below the Fermilevel.We have probed such states with magneto-luminescenceexperiments performed on 2DEG confined in aCdTe/CdMgTe quantum well. Focusing on the results oflow temperature experiments (100 mK) we investigate theenergy positions of σ + and σ − luminescence peaks relatedto fully occupied electronic 0th Landau level. The difference∆ between energies of these peaks is clearly notmonotonic with the magnetic field in contrast to the lineardependence expected when neglecting the effects ofelectron-electron interactions. As can be deduced fromfigure 36, we find that the oscillatory component of ∆ isproportional to the spin polarization of the 2DEG. Notably,∆ = g e f f µ B B when spin polarization vanishes (at even fillingfactors). g e f f = 1.3 corresponds well to the combinedelectron-hole bare g-factor in our structure. Effects ofelectron-electron interactions are therefore concluded toaffect the spin splitting of fully occupied Landau levels locateddeep below the Fermi level and not only those in thevicinity of the Fermi energy.Figure 35: Scheme of Landau levels of a two-dimensional electrongas at even (6) and odd (5) filling factors. Electron-electroninteraction is known to enhance the spin splitting at the Fermienergy if Landau level filling factor is odd. Enhanced or notenhanced spin splitting of fully occupied levels, deep below theFermi level, can be probed with polarization resolved magneto-luminescenceexperiments.Figure 36: a,b) Luminescence spectra of a 2DEG confined ina 20 nm-wide modulation doped CdTe quantum well at two distinctmagnetic field corresponding to Landau level filling factor 5(a) and 4 (b). Note that spin splitting of the main peak is larger atsmaller field. c) Energy positions of the main σ + and σ − luminescencepeaks and their separation, ∆ as a function of the magneticfield. Note the increase of ∆ each time the Landau filling is odd.J. Kunc, K. Kowalik, F.J. Teran, P. Plochocka, D.K. Maude, M. PotemskiG. Karczewski, T. Wojtowicz (Institute of Physics, Polish Academy of Sciences, Warsaw, Poland)29