论文标题
内部皮肤对非拓扑拓扑分形的影响
Inner Skin Effects on Non-Hermitian Topological Fractals
论文作者
论文摘要
非热（NH）晶体，准晶体和无定形网络显示出与真空的特定界面之一附近的宏观数量状态的积累，例如边缘，表面，铰链或角。该现象称为NH皮肤效应，只能在开放的边界条件下观察到。在这方面，自相似的分形，表现在系统内部的内部边界，具有一种新颖的现象，即\ emph {ninter {Inner Skin Effect}（ISE）。然后，NH皮肤效应出现在具有周期性边界条件的分形晶格的内边界。我们通过在代表性的平面Sierpinski地毯分形晶格上实施NH绝缘子和超导体的突出模型来展示这一观察结果。它们分别在内边缘和角落适合一阶和二阶ISE，用于充电和中性主要植物费。此外，超过扩展的参数式iSE与非平凡的散装拓扑结合，产生内在的ISES。随着最近在高度可调的超材料平台上的工程NH拓扑阶段的成功，例如光子和语音晶格以及倒出电路，至少在具有周期性边界条件的分形超材料上，可以在实验上观察到拟议的ISES。
Non-Hermitian (NH) crystals, quasicrystals and amorphous network display an accumulation of a macroscopic number of states near one of its specific interfaces with vacuum, such as edge, surface, hinge or corner. This phenomenon is known as the NH skin effect, which can only be observed with open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in the interior of the system, harbor a novel phenomenon, the \emph{inner skin effect} (ISE). Then the NH skin effect appears at the inner boundaries of the fractal lattice with periodic boundary condition. We showcase this observation by implementing prominent models for NH insulators and superconductors on representative planar Sierpinski carpet fractal lattices. They accommodate both first-order and second-order ISEs at inner edges and corners, respectively, for charged as well as neutral Majorana fermions. Furthermore, over extended parameter regimes ISEs are tied with nontrivial bulk topological invariants, yielding intrinsic ISEs. With the recent success in engineering NH topological phases on highly tunable metamaterial platforms, such as photonic and phononic lattices, as well as topolectric circuits, the proposed ISEs can be observed experimentally at least on fractal metamaterials with periodic boundary condition.
