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By means of CW polarization-resolved photoluminescence spectroscopy wedemonstrate the sign inversion of $g_z$-component of 2D electron g-factor withnarrowing of a hosting GaAs/Al$_{0.33}$Ga$_{0.67}$As quantum well (QW). Theenergy splitting between spectral lines correspoding to recombination from theelectron lowest Landau level and possessing opposite curcular polarization isanalyzed. Due to exchange interaction, this value reveals maximum or minimum asa function of magnetic field strength in the vicinity of electron fillingfactor $\nu=3$. The actual type of extremum depends on the electron$g_z$-component sign. The method allows to detect the sign inversion ofelectron Lande g-factor with its absolute value changing by less than $\Delta g\approx 0.06$. The reversal happens at a QW width of ($65\pm 3$ \AA).

Detection of 2D electron g-factor sign inversion in narrow GaAs/AlGaAs quantum wells