Abstract
We present a calculation of exciton states in semiconductor coupled quantum wells in the presence of electric and magnetic fields applied perpendicular to the QW plane. The exciton Schrödinger equation is solved in real space in three-dimensions to obtain the Landau levels of both direct and indirect excitons. Calculation of the exciton energy levels and oscillator strengths enables mapping of the electric and magnetic field dependence of the exciton absorption spectrum. For the ground state of the system, we evaluate the Bohr radius, optical lifetime, binding energy and dipole moment. The exciton mass renormalization due to the magnetic field is calculated using a perturbative approach. We predict a non-monotonous dependence of the exciton ground state effective mass on magnetic field. Such a trend is explained in a classical picture, in terms of the ground state tending from an indirect to a direct exciton with increasing magnetic field.
Highlights
Spatially-indirect excitons in coupled quantum wells (CQWs) present a model system for the study of a statistically degenerate Bose gas in solid-state materials
Neglecting non-parabolicity of the exciton band, which would be accounted for by treating the 2nd term in higher perturbation orders, we find the correction to the exciton energy proportional to P 2 and renormalized effective mass Mk∗,m of exciton state |k, m in magnetic field: 2e 2 | k, m |P·A(ρ)| j, m + s |2
We identify two limiting cases: Firstly, for small electric fields (F < 3 kV/cm) where the exciton ground state is predominantly direct, there is a monotonic increase of the effective mass with increasing magnetic field
Summary
Spatially-indirect excitons in coupled quantum wells (CQWs) present a model system for the study of a statistically degenerate Bose gas in solid-state materials. Several works ([46, 47] for example) used variational methods to study indirect excitons in magnetic fields These all lacked a calculation of the effective mass enhancement. The mass renormalization in the 2D limit was calculated for excitons in single QWs [49] and indirect excitons in double QWs [50] In those works, the electron and hole wave functions in the QW growth direction were approximated by delta functions located at the QW positions. The electron and hole wave functions in the QW growth direction were approximated by delta functions located at the QW positions This corresponds to the limit of infinitely deep QWs of zero width and is applicable only for the analysis of either purely direct or purely indirect excitons in the case of high electric field and strong QW confinement.
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