Effects of the Coulomb interaction on intersubband doubling and difference-frequency mixing in asymmetric double quantum wells

We study theoretically the influence of the direct and indirect Coulomb int eraction on second-harmonic generation (SHG) and difference-frequency gener ation (DFG) connected with intersubband transitions in asymmetric double qu antum wells. Our approach is based on the time-dependent local density appr oximation. The exact analytical expressions have been derived for SHG (in a two-subband system) and DFG (in a three-subband system) surface susceptibi lities. Unlike in our previous papers, we take into account the nonresonant terms and nonlinear dependence of the exchange-correlation potential upon the electron density. Numerical calculations have been performed for GaAl/A lGaAs asymmetric coupled double-quantum-well structures with small energy s eparation (about 10 meV) between the ground and excited subband when the ef fect of the Coulomb interaction is most pronounced and the nonresonant term s become essential. The results obtained show that Coulomb interaction not only shifts the peak positions in SHG and DFG spectra, but also modifies th eir height. The height modification can be particularly strong (even more t han one order of magnitude) in the case of the SHG. The nonlinearity of the exchange-correlation potential is found to lead to a novel feature that ca nnot be ignored in a correct description of SHG and DFG spectra. The electr on-density dependence of the many-body effect is analysed. A critical compa rison of the results obtained with those reported in the literature is also given.