Free-electron gas in the Apollonian network: multifractal energy spectrum and its thermodynamic fingerprints.
Free-electron gas in the Apollonian network: multifractal energy spectrum and its thermodynamic fingerprints.
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DOI：
10.1103/physreve.79.016104
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发表时间：
2009-01
期刊：
影响因子：
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通讯作者：
I. N. de Oliveira;F. D. de Moura;M. Lyra;J. S. Andrade;E. L. Albuquerque
中科院分区：
文献类型：
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作者：
I. N. de Oliveira;F. D. de Moura;M. Lyra;J. S. Andrade;E. L. Albuquerque
我们研究紧束缚框架内阿波罗网络中的自由电子气体。众所周知，底层晶格的无标度和小世界特征会产生具有三角形奇点、间隙和迷你带的相当结构化的能谱。在对有限代数的网络相应邻接矩阵进行精确数值对角化之后，我们采用状态密度矩的缩放分析来表征其多重分形并报告相关的奇点谱。能谱的分形性质也通过对比热的温度依赖性的对数调制反映在热力学行为中。由于电子和空穴的热激发，阿波罗网络不存在手性对称性，从而导致不同的热力学行为。
We study the free-electron gas in an Apollonian network within the tight-binding framework. The scale-free and small-world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities, gaps, and minibands. After an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations, we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum. The fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat. The absence of chiral symmetry of the Apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations.