Bulk-local-density-of-state correspondence in topological insulators

Abstract

In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states.

Current approaches to distinguish topological phases from topologically-trivial phases have limited general applicability. Here, in a photonic-crystal context, the authors demonstrate that in trivial structures the bulk local density of states (LDOS) extends all the way to the edges and corners, while in topological structures the bulk LDOS actually avoids the edges and corners.