Electronic wave functions of quasiperiodic systems in momentum space
Electronic wave functions of quasiperiodic systems in momentum space
复制标题
动量空间中准周期系统的电子波函数
DOI：
10.1140/epjb/e2013-40261-6
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Schreiber
中科院分区：
文献类型：
--
作者：
S. Rolof;S. Thiem;M. Schreiber
在准晶镶嵌中，经常可以发现多重分形电子波函数。为了更好地了解它们的局域特性，我们研究了动量空间中准周期平铺的波函数。该模型基于一维准周期链，其中原子通过根据金属平均序列排列的弱键和强键耦合。然后，d 维中相关的超立方平铺和迷宫平铺由 d 个此类链的直接乘积构造而成。结果表明，每个波函数都由波矢量层次来描述，并且总是由与波函数的能量本征值直接相关的单个波矢量主导。系统相应的谱函数显示了具有不同强度的分支的层次结构。每个分支都是主分支的副本，包含每个波函数的主波矢量。使用微扰理论和重正化群方法，我们确定了弱耦合和强耦合极限的分支形状。
In quasicrystalline tilings often multifractal electronic wave functions can be found. In order to obtain a better insight into their localization properties, we study the wave functions of quasiperiodic tilings in momentum space. The models are based on one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated hypercubic tilings and labyrinth tilings in d dimensions are then constructed from the direct product of d such chains. The results show that each wave function is described by a hierarchy of wave vectors and is always dominated by a single wave vector which is directly related to the energy eigenvalue of the wave function. The corresponding spectral function of the systems shows a hierarchy of branches with different intensities. Each branch is a copy of the main branch containing the dominant wave vectors for each wave function. Using perturbation theory and a renormalization group approach, we determine the shape of the branches for the limit of weak and strong coupling.