弱电场作用下Fibonacci超晶格电子态的多重分形分析
Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields
摘要：
研究了弱电场对Fibonacci超晶格电子结构的影响。电场使非周期超晶格的能谱产生非线性动力学。从能级反交叉的角度解释了非线性的机理。应用多重分形理论研究了弱电场对电子本征函数统计性质的影响。结果表明，外加电场并没有消除电子本征函数的多重分形特征，奇异谱仍然是非抛物线的，但具有修改的形状。在弱电场中，相邻本征态能级间距离的变化导致相应本征函数参与率的倒数变化。它表明，反交叉附近的反参与比的局部极小值对应于奇异性强度的边缘值之间的差异的一阶导数的不连续性。作为电场的函数的广义维数的分析表明，电场相关的反交叉附近的相邻的电子本征函数振幅的空间波动，和标度指数的非线性字符确认相应的电子本征函数的多重分形。
英文摘要：
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.
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