Self-dual quasiperiodic systems with power-law hopping
Self-dual quasiperiodic systems with power-law hopping
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DOI：
10.1103/physrevb.96.054202
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发表时间：
2017-06
影响因子：
3.7
通讯作者：
S. Gopalakrishnan
中科院分区：
文献类型：
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作者：
S. Gopalakrishnan
我们引入并探索了一类准周期势中单粒子运动的自对偶模型，其跳跃幅度与指数p呈幂函数关系。这些模型是常见的Aubry-Andre模型的推广。对于足够大的$p$，它们的静态性质类似于Aubry-Andre模型，尽管局域相中的低频电导率对$p$很敏感。对于$p\leq 2.1$，Aubry-Andre局域化转变分为三个转变；在Aubry-Andre模型的自对偶点附近出现了两个不同的中间区域，既有局域态又有离域态。在中间区域，态的密度在大部分光谱中是奇异连续的，并且近似是自相似的：态形成窄的能带，这些能带被分成更窄的子带；我们没有发现明显的迁移率边缘的迹象。当$p<；1$时，局域态在无规势中是不稳定的；然而，在本模型中，对于相对较大的系统，存在紧密的局域态。我们讨论了低频光学电导率的频率依赖性和强烈的样本间波动，尽管当幂定律缓慢衰减时，恢复了Mott定律的适当推广版本。我们提出的证据表明，这些特征中的许多都存在于远离自我二元性的模型中。
We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar Aubry-Andre model. For large enough $p$, their static properties are similar to those of the Aubry-Andre model, although the low-frequency conductivity in the localized phase is sensitive to $p$. For $p \leq 2.1$ the Aubry-Andre localization transition splits into three transitions; two distinct intermediate regimes with both localized and delocalized states appear near the self-dual point of the Aubry-Andre model. In the intermediate regimes, the density of states is singular continuous in much of the spectrum, and is approximately self-similar: states form narrow energy bands, which are divided into yet narrower sub-bands; we find no clear sign of a mobility edge. When $p < 1$, localized states are not stable in random potentials; in the present model, however, tightly localized states are present for relatively large systems. We discuss the frequency-dependence and strong sample-to-sample fluctuations of the low-frequency optical conductivity, although a suitably generalized version of Mott's law is recovered when the power-law is slowly decaying. We present evidence that many of these features persist in models that are away from self-duality.