Strictly localized states on a two-dimensional Penrose lattice.
Strictly localized states on a two-dimensional Penrose lattice.
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二维彭罗斯晶格上的严格局域态。
DOI：
10.1103/physrevb.38.1621
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Kohmoto
中科院分区：
文献类型：
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作者：
Masao Arai;T. Tokihiro;T. Fujiwara;M. Kohmoto
在原子轨道位于菱形顶点的紧束缚模型中研究了二维彭罗斯晶格上能量 E= 0 的无限简并态。 E=0的状态都是严格定域的，仅在某些特定顶点上有振幅，这些顶点是三边顶点和一些非三边顶点。分析计算出它们分数的下界为-50τ+ 81≊ 9.83× 10− 2 [τ=(√ 5+ 1)/2]，推测这是精确分数。
Infinitely degenerate states at an energy E= 0 on a two-dimensional Penrose lattice are investigated in a tight-binding model where atomic orbitals are located at vertices of rhombuses. The states with E= 0 are all strictly localized and have amplitudes only on some specific vertices, which are three-edge vertices and some non-three-edge vertices. A lower bound on the fraction of them is calculated analytically as-50τ+ 81≊ 9.83× 10− 2 [τ=(√ 5+ 1)/2], which is conjectured to be the exact fraction.