AC Conduction in Quasiperiodic Lattices
- PDF / 406,584 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 102 Downloads / 194 Views
AC Conduction in Quasiperiodic Lattices Chumin Wang, Raúl Oviedo-Roa, Vicenta Sánchez, and Luis A. Pérez Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, C.P. 04510, México D.F. MEXICO. ABSTRACT The electronic transport in Fibonacci lattices at zero temperature is studied by means of the Kubo-Greenwood formula within the tight-binding scheme, where a renormalization process capable to address the electrical conductivity in macroscopic quasiperiodic systems is used. The effects of the Fermi-energy location on the ac conductivity are analyzed in detail for a wide range of the system sizes. Special attention is paid to the transparent states, whose transmission coefficient is unity. The results show a rapid decay of their ac conductivity as the frequency increases in comparison with that of periodic systems, and the spectra scale with the inverse of the system size as occur in periodic ones, where analytical results are obtained. Furthermore, a new low-frequency minimum appears when the inhomogeneity of the Fibonacci lattice grows. INTRODUCTION The localization and transport of electrons in quasiperiodic systems have been an interesting and controversial issue, since the discovery of quasicrystalline alloys in 1984. Nowadays, there is a consensus that the eigenvalue spectrum produced by a quasiperiodic potential is singular continuous and the associated eigenfunctions are critical [1]. Moreover, the level statistics show an inverse-power-law level-spacing distribution [2], neither Wigner nor Poisson ones. Hence, the electrical conduction of these critically localized states becomes an especially interesting subject. In particular, Fibonacci quasiperiodic superlattices have been built [3] and their properties can be well understood by means of simple models [4]. The hopping conductivity in Fibonacci chains has been addressed by using the Miller-Abrahams equations [5] and the optical conductivity has been analyzed recently within a generalized Drude formula [6]. On the other hand, transparent states with unity transmission coefficient have been found [7] in mixing Fibonacci systems (MFS) and their ac conductivity has been studied by using the Kubo-Greenwood formula [8]. In general, a good probe of the nature of the electronic eigenvalue spectrum and the localization of wave functions is the ac electrical conductivity at zero temperature, since it depends not only on the states at the Fermi level but also on the global structure of the spectrum. In Ref. [8] the electrical conductivity for two different MFS with k=2 and 3, as defined in Ref. [9], has been studied. However, the effects of the Fermi-energy location and the system inhomogeneity on the ac conductivity are not widely analyzed in the literature. In this work, we investigate three different MFS within k=3 and report a system-size scale invariance and a new minimum of the Fibonacci ac conductivity which deepens when the system becomes more inhomogeneous. DENSITY OF STATES AND DC CONDUCTIVITY A mixing Fibo
Data Loading...
