Finite-size Topology

Abstract

We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-\delta$ dimensions and finite in size in $\delta$ dimensions, is fundamentally different from that of systems thermodynamically large in all $D$-dimensions: as $(D-\delta )$-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 $\delta +1$ topological invariants, ranging from the $D$-dimensional topological invariant to the $(D-\delta )$-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.

arXiv comment9 pages, 8 figures, v2: accepted version

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Cited by in corpus (10)

• Time-reversal invariant finite-size topology
• Quantum skyrmion Hall effect
• Multiplicative Majorana zero-modes
• Finite-size topological phases from semimetals
• Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz
• Emergent topology in thin films of nodal line semimetals
• Crystalline finite-size topology
• Observable-enriched entanglement
• Confinement-induced Majorana modes in a nodal topological superconductor
• Multiplicative Chern insulator