论文标题
有限尺寸的拓扑
Finite-size Topology
论文作者
论文摘要
我们表明，在$ d $维系统中，拓扑表征和分类仅在$ d-δ$尺寸中仅在热力学上大，并且在$δ$尺寸的大小中有限，与所有$ d $ dimensions中的热力学上的系统大不相同。杂交以创建新颖的拓扑阶段，其特征在于一组$δ+1 $拓扑不变的，从$ d $二维拓扑不变到$（d-δ）$ - 维度拓扑不变性。该系统表现出拓扑响应特征和由这些拓扑不变值组合的组合所控制的拓扑响应特征，并具有较低维度的拓扑拓扑，表征了系统热力学在所有$ d $ dimmimentions中较大的系统热力学拓扑阶段的碎片。我们为范式Chern绝缘子阶段展示了这种物理学，但是通过更广泛的拓扑系统满足了其实现的要求。
We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-δ$ dimensions and finite in size in $δ$ dimensions, is fundamentally different from that of systems thermodynamically large in all $D$-dimensions: as $(D-δ)$-dimensional topological boundary states permeate into a system's $D$ dimensional bulk with decreasing system size, they hybridize to create novel topological phases characterized by a set of $δ+1$ topological invariants, ranging from the $D$-dimensional topological invariant to the $(D-δ)$-dimensional topological invariant. The system exhibits topological response signatures and bulk-boundary correspondences governed by combinations of these topological invariants taking non-trivial values, with lower-dimensional topological invariants characterizing fragmentation of the underlying topological phase of the system thermodynamically large in all $D$-dimensions. We demonstrate this physics for the paradigmatic Chern insulator phase, but show its requirements for realization are satisfied by a much broader set of topological systems.
