Electronic spectrum and localization of electronic states in aperiodic quantum dot chains
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ONIC PROPERTIES OF SOLID
Electronic Spectrum and Localization of Electronic States in Aperiodic Quantum Dot Chains P. Yu. Korotaev*, Yu. Kh. Vekilov, and N. E. Kaputkina National University of Science and Technology “MISiS,” Leninskii pr. 4, Moscow, 119049 Russia *email: [email protected] Received July 28, 2013
Abstract—The electronic energy spectra of aperiodic Thue–Morse, Rudin–Shapiro, and doubleperiodic quantum dot chains are investigated in the tightbinding approximation. The dependence of the spectrum on all parameters of a “mixed” aperiodic chain model is studied: the electronic energy at quantum dots and the hopping integrals. The electronic degree of localization in the chains under consideration is determined by analyzing the inverse participation ratio. Its spectral distribution and the dependence of the bandaveraged degree of localization on these model parameters have been calculated. It is shown that a transition of the sys tem’s sites to a resonant state in which the degree of electron localization decreases, while an overlap between the subbands occurs in the spectrum is possible when the parameters are varied. DOI: 10.1134/S1063776114010087
1. INTRODUCTION An aperiodic system is a system whose elements or properties are distributed in a certain but not periodic order. Such structures, for example, layered materials, are currently being actively studied and applied in electronics, optics, and laser technology. Compared to periodic counterparts, their peculiarities include a complex fragmented spectrum, sharp conductivity peaks, the existence of critical states, and additional types of symmetry [1]. Another important peculiarity of aperiodic systems is that they provide additional degrees of freedom to obtain the required properties, i.e., the properties of a system can be changed signifi cantly by changing the aperiodic law according to which its elements are distributed. In addition, the properties of an aperiodic system are greatly affected by a change in its parameters (for example, a change in the thickness of the layers or the material from which they were fabricated) even within the framework of a single aperiodic law. Of course, various objects can be arranged in an aperiodic order. Here, we consider aperiodic chains of quantum dots in the tightbinding approximation. We study how the electronic spectrum and transport prop erties of such systems are affected by varying their parameters: the electronic energy at a quantum dot, the coupling between quantum dots, the system’s sizes, and the type of aperiodic law. As far as we know, there is no such investigation at present. In addition, the simplified onsite and transfer models were mainly considered [2–5], while here we consider a mixed model of an aperiodic system (see below). The mixed model of a Thue–Morse chain was studied in [6], but
the spectrum and the degree of electron localization when varying the parameters were not analyzed. A certain aperiodic sequence corresponds to the aperiodic order in which the system’s elements
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