Fibonacci superlattices of narrow-gap III-V semiconductors

We report the theoretical electronic structure of Fibonacci superlattices of narrow-gap III-V semiconductors. The electron dynamics is accurately described within the envelope-function approximation in a two-band model. Quasiperiodicity is introduced by considering two different III-V semiconductor layers and arranging them according to the Fibonacci series along the growth direction. The resulting energy spectrum is then found by solving exactly the corresponding effective-mass (Dirac-like) wave equation using transfer-matrix techniques. We find that a self-similar electronic spectrum can be seen in the band structure. Electronic transport properties of samples are also studied and related to the degree of spatial localization of electronic envelope functions via the Landauer resistance and Lyapunov coefficient. As a working example, we consider type II InAs/GaSb superlattices and discuss in detail our results in this system.