Electronic Properties of Fibonacci Quasi-Periodic Heterostructures

Abstract

73.21.Fg We study the electronic states of GaAs-AlAs Fibonacci heterostructures grown along the (001) direction. We employ an empirical tight-binding Hamiltonian including spin-orbit coupling together with the surface Green's function matching method. We present results for the L point of the finite eighth Fibonacci generation. We compare these results with those of the constituent quantum wells. No Fibonacci spectrum is found in the energy regions studied, but broad bands with different spatial localization in different energy ranges. IntroductionThe physical properties of quasi-periodic systems have been studied intensively in the last years . The interest was mainly coming from the theoretical side by the prediction that these systems should manifest non-conventional electron and phonon states [9,11,23,25] exhibiting energy spectra with a high fragmentation and fractal character [7,17,24]. The experimental growth of Fibonacci [2, 3] and ThueMorse [4] multilayered systems has provided the practical realization of these systems. The Fibonacci system, a linear lattice constructed recursively, is the one-dimensional (1D) version of the quasi-crystals, and it has been the subject of intensive theoretical study as a model of the quasi-crystals. The electronic structure of the Fibonacci system has been investigated mainly in the single-band tight-binding limit. In these studies, it was found that the energy spectrum is self-similar, and the energy band divides into three subbands, each of which further subdivides into three, and so on [13-16], thus producing a singular continuous spectrum [21], which in the infinite limit reduces to a Cantor-like spectrum [17] with dense energy gaps everywhere [7][8][9][10]. A much more realistic study was presented in Ref.[28] by using an empirical tight-binding (ETB) sp 3 s * Hamiltonian [35], with no spin-orbit coupling, and arranging one monolayer of GaAs and one monolayer of AlAs in a Fibonacci sequence. The authors of Ref.[28] obtained the electronic structure of a superlattice having as period a 12th Fibonacci generation, containing 144 GaAs and 89 AlAs monolayers. Fibonacci generations ranging from the second to the fifth, but including more monolayers in each constituent block, were studied in Refs. [29,30] by using a similar ETB Hamiltonian, now including the spin-orbit coupling [36]. It was found in these more realistic studies [28][29][30] that the Fibonacci spectrum could only be observed for some energy ranges and for wavevectors in the vicinity of the superlattice G point. It was found also that the lower conduction and higher valence bands exhibited a selective spatial localization in the thickest GaAs slabs forming the superlattices. In Refs. [32,33], Fibonacci, Thue-Morse, and Rudin-Shapiro finite multilayered systems were studied by using models similar to those of Refs. [29,30] including different types of building blocks. It was found that the

Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields

“…Experimental as well as theoretical studies of these superlattices are concentrated on the consequences of the long-range correlations induced by the aperiodic arrangement at a length scale longer than atomic one [24,25]. In particular, this problem has been extensively investigated in the Fibonacci superlattices which are regarded as a typical example of aperiodic systems [26,27,28]. In these studies, it has been found that the wave functions of one-particle states are critical, i.e.…”

Self-similar optical transmittance for a deterministic aperiodic multilayer structure

“…Merlin et al [2] were the first to grow a Fibonacci lattice of GaAs and AlAs and they studied its x-ray diffraction and Raman scattering properties. Since then, many other interesting studies of propagation of electrons, electromagnetic waves and acoustic waves have been reported in quasiperiodic multi-layered onedimensional structures with several profiles like those of Fibonacci, Cantor, Rudin-Shapiro, Thue-Morse, and others [3][4][5]. Of particular interest is the understanding of the optical propagation, localization and transmission of optical waves in this type of structures, which are different from the periodic or random structures due to the long correlation effects induced by the quasiperiodicity [6].…”

“…These multilayers may have promising technological applications in non-linear optics as well as in the design of optical devices like soft x-ray filters, efficient photovoltaic solar cells [6][7][8], etc. In this work we propose a model for a new aperiodic multilayer whose refractive index is modulated by a deterministic numerical 3 Author to whom any correspondence should be addressed. sequence named 'the 1s-counting sequence', formed by the number of 1s in the binary representation of the natural numbers [9].…”

Transmission of electrons in a finite superlattice with a Pascal's Triangle profile

“…There are many studies of propagation of electrons, electromagnetic waves and acoustic waves in quasi-periodic multilayered one-dimensional structures with several profiles like those of Fibonacci, Cantor, Rudin-Shapiro, Thue-Morse, etc. [6][7][8]. The numerical sequence formed by the quantity of odd numbers in each row of the Pascal's Triangle, has the property of self-similarity.…”