Aubry-Andre-Harper model: multifractality analysis versus Landauer conductance for quasicrystal chains

Abstract

We present the result of the localization feature of the quasiperiodic Aubry-Andre model. Localization and delocalization of energy eigenstates of the system are investigated by taking into account well-known theoretical perspectives such as the fractal dimension and the Landauer formula. Energy spectra of the system are obtained in the form of a Hofstadter butterfly for different values of the incommensurate parameter of the Aubry-Andre model and different values of the quasiperiodic disordered potentials. The inverse participation ratio analysis and fractal analysis of conductance are used for describing the localization feature of energy eigenstates. The conductance of the eigenstates is also obtained by calculating the transmission eigenvalues in the Landauer picture.