Electric-field-induced strong mixing betweene1−hh1ande1−hh2excitons in asymmetric double quantum wells

Abstract

We analyze the electric-field-dependent strong mixing of the two near band-edge ground-state excitons in asymmetric double quantum wells (ADQWs). This excitonic mixing is mainly attributed to the Coulomb interactions between subbands and the valence-subband nonparabolicity. The effect of mixing on the energy levels and oscillator strengths is obtained by a comparison of results including and excluding the Coulomb interaction between different subband pairs which appears in the off-diagonal matrix elements of the Hamiltonian in the calculation of exciton states. We find that a substantial portion of the oscillator strength of the $e1\text{\ensuremath{-}}hh1$ ground-state exciton is due to the $e1\text{\ensuremath{-}}hh2$ subband pair in a bias range of the anticrossing region between pairs of valence subbands. Results also show that excluding the excitonic mixing effect results in significant error in both the energies and the oscillator strengths of the excitons in an ADQW with a thick barrier $(3\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. Even in an ADQW with a fairly thin barrier $(1.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, the error in the oscillator strengths can be substantial, although the errors in the computed energies may be tolerable. Detailed analysis of ${k}_{\ensuremath{\Vert}}$-dependent Coulomb matrix elements and exciton expansion coefficients reveals that neglecting the off-diagonal elements in the exciton Hamiltonian diminishes the contribution of the ${k}_{\ensuremath{\Vert}}$-dependent subband envelopes around the anticrossing in ${k}_{\ensuremath{\Vert}}$ space to the corresponding excitons. Further, it is demonstrated that the application of almost-degenerate perturbation theory to the uncoupled excitons with the intention of accounting for this mixing effect is to be approached with caution.