论文标题
penrose准晶体中受保护的零能状态的性质
Nature of Protected Zero Energy States in Penrose Quasicrystals
论文作者
论文摘要
penrose菱形晶体的电子光谱表现出完全退化的零能量状态的宏观分数。与其他两部分准晶体（例如风筝和式）相反，这些零能状态不能归因于两个构成准晶体的sublattices中的地点数量之间的全局不匹配$Δn$。在这里，我们认为这些零能状态与局部不匹配$Δn（\ bf r）$有关。尽管$Δn（\ bf r）$平均为零，但自组织域的交错平均值给出了正确数量的零能量状态。从物理上讲，局部不匹配与支持零能量状态的嵌套自相似域的隐藏结构有关。这使我们能够制定一个真实的空间统计组方案，该方案为零能量状态的比例定律，$ z $，$ n $，$ n $，as $ z \ propto n^{ - η} $带有$η= 1- \ ln 2/\ ln 2/\ ln（1+τ）$ 0.2798 $（$ 0.2798 $）（$ n = 1 $ 0.2798 $）。它还重现了零能状态的已知总数，$81-50τ\约0.0983 $。我们还表明，这些状态的确切退化性受到保护，免受多种局部扰动的影响，例如不规则或随机跳振幅，磁场，晶格的随机稀释等。我们将这种鲁棒性归因于隐藏的域结构，并推测其潜在的拓扑原点。
The electronic spectrum of the Penrose rhombus quasicrystal exhibits a macroscopic fraction of exactly degenerate zero energy states. In contrast to other bipartite quasicrystals, such as the kite-and-dart one, these zero energy states cannot be attributed to a global mismatch $Δn$ between the number of sites in the two sublattices that form the quasicrystal. Here, we argue that these zero energy states are instead related to a local mismatch $Δn(\bf r)$. Although $Δn(\bf r)$ averages to zero, its staggered average over self-organized domains gives the correct number of zero energy states. Physically, the local mismatch is related to a hidden structure of nested self-similar domains that support the zero energy states. This allows us to develop a real space renormalization-group scheme, which yields the scaling law for the fraction of zero energy states, $Z$, versus size of their support domain, $N$, as $Z\propto N^{-η}$ with $η=1-\ln 2/\ln(1+τ) \approx 0.2798$ (where $τ$ is the golden ratio). It also reproduces the known total fraction of the zero energy states, $81-50τ\approx 0.0983$. We also show that the exact degeneracy of these states is protected against a wide variety of local perturbations, such as irregular or random hopping amplitudes, magnetic field, random dilution of the lattice, etc. We attribute this robustness to the hidden domain structure and speculate about its underlying topological origin.
