Electronic transport in k-component Fibonacci quantumwaveguides

Abstract

We present a study of electronic behaviours in the k-componentFibonacci (KCF) quantum waveguides, in which k differentincommensurate intervals are arranged according to a substitutionrule. On the basis of the transfer matrix method, the quantum transmissionproperties of the KCF stub structures are obtained. It is shownthat the transmission coefficient depends on the wavevector ofthe electron and the number of different incommensurate intervals k.For the KCF waveguides with the same k, on increasing thenumber of stubs, the minima in transmission extend gradually intothe band gap over which the transmission is blocked. Meanwhile moretransmission peaks appear. For finite KCF stub structures, onincreasing the number of different incommensurate intervals k, thetotal transmission over the spectral region of interest decreasesgradually and the width of the electronic band gap is enlarged.Moreover, when the value of k is large enough, the transmission isbasically shut off, except at a few energies where resonanttunnelling takes place. These properties make it possible to usethis kind of KCF waveguide as a switching device for digitalapplications. On the other hand, the charge-density distributionsin these structures are singularly continuous. We propose that theycan be analysed using a multifractal concept. A dimensional spectrumof singularities associated with the charge density, f (α),demonstrates that the electronic transport in the KCF waveguidepresents scaling properties; hence the charge-density distributionshows a genuine multifractality.