Effect of an in-plane magnetic field on the electronic states and intraband transitions in quasi-periodic Fibonacci superlattices

Abstract

Quasi-periodic GaAs-(Ga,Al)As Fibonacci superlattices under in-plane magnetic fields are studied within the effective-mass approximation. Electron-envelope wavefunctions, magnetic subbands and intraband transition strengths are obtained using a parabolic model for the conduction band, and via an expansion in harmonic-oscillator wavefunctions. Calculations are performed for magnetic fields related by integer powers of the golden mean tau =(1+512/)/2. It is shown that, for magnetic field values scaled by tau 2n, the corresponding magnetic levels, electron wavefunctions and transition strengths essentially exhibit a self-similar or anti-self-similar behaviour as appropriate for a GaAs-(Ga,Al)As Fibonacci superlattice. Also, for a given magnetic field, the interband transition strengths have similar properties to those found for the case of periodic superlattices. The intraband absorption coefficients are calculated for magnetic field values scaled by tau 2n, and theoretical absorption spectra, when properly scaled, are shown to be self-similar (for even n) or anti-self-similar (for odd n), a result which could be experimentally verified in n-doped GaAs-(Ga,Al)As Fibonacci superlattices.