分形化金属
Fractalized Metals
AI总结：
本文研究分形晶格中非相互作用费米子的拓扑相，发现均匀分形晶格中不存在有能隙拓扑相，而是出现一种低能态分层排列的新型金属态——分形化金属，并证明其手性输运对无序具有鲁棒性。
摘要：
非相互作用费米子的有能隙相的分类依赖于十重对称性和空间维度。维度的概念导致了体态与边缘之间明确的划分。在这里，我们探索了体态与边缘区分模糊的系统中拓扑相的性质，分形晶格是这类系统的典型例子。我们的关键发现是，在均匀分形晶格（其中每个格点具有相同的配位数）中，不存在有能隙的拓扑相。取而代之的是一种新颖的金属态——分形化金属——其低能态在承载它们的分形结构上分层排列。我们研究了这种金属的性质（例如手性输运），并证明了它对无序的鲁棒性。此外，通过研究多种分形模型，我们确立了分形的均匀性是实现这种分形化金属态的关键条件。
英文摘要：
The classification of gapped phases of non-interacting fermions hinges on the tenfold symmetries and on the spatial dimension. The notion of dimension leads to a well defined demarcation between bulk and edge. Here we explore the nature of topological phases in systems where the distinction between bulk and edge is nebulous, of which fractal lattices are canonical examples. Our key finding is that in homogeneous fractal lattices (where every site is equally coordinated), there are no gapped topological phases. What appears instead is a novel metallic state -- the fractalized metal -- whose low energy states arrange hierarchically on the structure of the fractal that hosts them. We study the properties (such as chiral transport) of this metal and demonstrate its robustness to disorder. Further, by studying a variety of fractal models we establish that the homogeneity of the fractal is a key condition for the realization of such fractalized metallic states.
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