Renormalization approach to the electronic localization and transport in macroscopic generalized Fibonacci lattices

Abstract

Electronic transport and wavefunction localization are two closely related phenomena, but their behavior in truly macroscopic aperiodic lattices is a non-widely addressed issue. We study in this article the electrical conductivity of generalized Fibonacci (GF) lattices through the Kubo-Greenwood formula, while the localization of electronic wavefunction is analyzed by means of the Lyapunov exponent and participation ratio (PR). For periodic chains, an analytical expression of the Lyapunov exponent is obtained. We have also developed for the first time a real-space renormalization method to calculate the PR of macroscopic GF lattices described by tight-binding Hamiltonians. Moreover, we report a novel unified renormalization method for the Kubo-Greenwood formula applied to GF chains. For quasiperiodic lattices, the results reveal a power-law decay of the spectral averages for both PR and DC conductivity when the system length increases. In addition, we present a systematic analysis of the AC conductivity spectra observing truly large resonant peaks in comparison to the ballistic one. The electrical conductance of GF nanowires is also investigated. Finally, the results suggest that PR could not be proper for the analysis of critically localized states.