A full numerical calculation of the Franz--Keldysh effect on magnetoexcitons in a bulk semiconductor

We have performed a full numerical calculation of the Franz--Keldysh (FK)effect on magnetoexcitons in a bulk GaAs semiconductor. By employing aninitial value method in combination with the application of a perfect matchedlayer, the numerical effort and storage size are dramatically reduced due toa significant reduction in both computed domain and number of basefunctions. In the absence of an electric field, the higher magnetoexcitonicpeaks show distinct Fano lineshape due to the degeneracy with continuum statesof the lower Landau levels. The magnetoexcitons that belong to the zerothLandau level remain in bound states and lead to Lorentzian lineshape, because theyare not degenerated with continuum states. In the presence of an electricfield, the FK effect on each magnetoexcitonic resonance can be identified forhigh magnetic fields. However, for low magnetic fields, the FK oscillationsdominate the spectrum structure in the vicinity of the bandgap edge and themagnetoexcitonic resonances dominate the spectrum structure of higherenergies.In the moderate electric fields, the interplay of FK effect andmagnetoexcitonic resonance leads to a complex and rich structure in theabsorption spectrum.