2 research outputs found
Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields
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