hide
Free keywords:
Atomic physics; Boundary state; D dimensions; Dimensional systems; Finite size; Low dimensional; Response signatures; System size; Topological invariants; Topological phase; Topological response; Topology
Abstract:
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 nontrivial 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. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
