具有两个相互无公度调制频率的一维无公度链的电子态性质

ELECTRONIC STATE PROPERTIES OF AN ONE-DIMENSIONAL INCOMMENSURATE CHAIN WITH TWO MULTI-INCOMMENSURATE MODULATION FREQUENCIES

采用逐级有理数近似，通过对带宽和波函数的多分形谱ｆ（α＿ｌ）￣α＿ｌ的渐近行为的研究，探讨了一个具有两个相互无公度的调制频率Ｑ＿１和Ｑ＿２的一维无公度电子态模型：ε＿ｎ＝Ｖ＿０［ｃｏｓ（Ｑ＿１ｎ）＋ｃｏｓ（Ｑ＿２ｎ）］，其中Ｑ＿１＝２π／λ和Ｑ＿２＝２π／λ￣２，且，结果表明，除了个别边态的反常行为外，Ｖ＿０＜１．００时的本征态都是扩展态，Ｖ＿０＝１．００时的本征态都是中间态，而Ｖ＿０＞１．００的所有本征态都是局域态，即在Ｖ＿０＝１．００时存在一个金属－绝缘体转变。这种性质与Ａｕｂｒｙ模型十分相似。

The electronic state Properties of an one-dimensional incommensuratechain with two multi-incomensurate modulation frequencies are studied by analysing theasymptotic behaviors of the bandwidth and multifractal spectrum in successive rational ap-proximation.We have found that,except a few states in the band edges,the stases are ex-tended if V_0<1.00,the states are critical if V_0=1.00,ad the states are localized if V_0>1.00.That means there exists a metal-insulator trasition at V_0=1.00.This property is similarwith that of the Aubry model and it is a special case of the model for one-dimensionalincommensurate chain with two multi-incommensurate modulation frequencies.