Fibonacci superlattices of narrow-gap III-V semiconductors

Abstract

We report theoretical electronic structure of Fibonacci superlattices of narrow-gap III-V semiconductors. 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 tranfer-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 envelopefunctions via Landauer resistance and Lyapunov coefficient. As a working example, we consider type II InAs/GaSb superlattices and discuss in detail

Electric field effects in Fibonacci superlattices

“…Theoretical studies demonstrate that ideal aperiodic SLs should exhibit a highly-fragmented and fractal-like electronic spectrum [4,[9][10][11]. This self-similar spectrum is observable even when unintentional imperfections arising during the growth process are considered [12].…”

Can fractal-like spectra be experimentally observed in aperiodic superlattices?

“…One of the most appealing motivations for the experimental study of aperiodic superlattices (ASLs) arranged according to Fibonacci [1] and Thue-Morse [2] sequences is the theoretical prediction that these systems exhibit a highly-fragmented energy spectrum displaying self-similar patterns [3][4][5]. From a strict mathematical perspective, it has been proven that the spectra of both Fibonacci and Thue-Morse lattices are Cantor sets in the thermodynamic limit [6,7].…”

On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

“…In both cases all the atomic potentials are assumed to be equal ( = , ∀ ) and (9) reduces to Figure 12: Self-similarity in the energy spectrum of a InAs/GaSb Fibonacci superlattice. The left panel shows the whole spectrum for an order = 3 superlattice, whereas the central and right panels show a detail of the spectrum for superlattices of orders = 6 and = 9, respectively (from [47], with permission from IOP Publishing Ltd.).…”