Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields

TL;DR

This study investigates how weak electric fields influence the multifractal properties of electronic states in Fibonacci superlattices, revealing persistent multifractality and field-induced spectral and eigenfunction modifications.

Contribution

It demonstrates that weak electric fields do not destroy the multifractal nature of electronic eigenfunctions but alter their spectral and statistical properties, providing new insights into aperiodic quantum systems.

Findings

Electric field causes nonlinear energy spectrum dynamics.

Multifractality of eigenfunctions persists under weak electric fields.

Energy level anticrossings relate to changes in eigenfunction localization.

Abstract

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions.