Self-similarity and anti-self-similarity of the effective Landég⊥factor inGaAs−(Ga,Al)AsFibonacci superlattices under in-plane magnetic fields

Abstract

A theoretical study of the effects of in-plane magnetic fields on the Land\'e ${g}_{\ensuremath{\perp}}$ factor associated to conduction electrons in $\mathrm{GaAs}\text{\ensuremath{-}}(\mathrm{Ga},\mathrm{Al})\mathrm{As}$ Fibonacci superlattices is presented. We have used the Ogg-McCombe effective Hamiltonian, which includes nonparabolic and anisotropy effects, in order to describe the electron states in the Fibonacci heterostructure. We have expanded the corresponding electron envelope wave functions in terms of harmonic-oscillator wave functions, and obtained the Land\'e ${g}_{\ensuremath{\perp}}$ factor for magnetic fields related by even powers of the golden mean $\ensuremath{\tau}=(1+\sqrt{5})∕2$. Theoretical results for $\mathrm{GaAs}\text{\ensuremath{-}}(\mathrm{Ga},\mathrm{Al})\mathrm{As}$ Fibonacci superlattices, under magnetic-field values scaled by ${\ensuremath{\tau}}^{2n}$, clearly exhibit a self-similar (for even $n$) or anti-self-similar (for odd $n$) behavior for the Land\'e ${g}_{\ensuremath{\perp}}$ factors, as appropriate.