Subdimensional topologies, indicators, and higher order boundary effects
Gunnar F. Lange, Adrien Bouhon, Robert-Jan Slager
Abstract
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features. Within this context we recently reported on a class of unexplored topological structures that thrive on the concept of subdimensional topology. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within subdimensional spaces, such as planes or lines. This perspective does not just refine classification pursuits, but can result in observable features in the full dimensional sense. In three spatial dimensions (3D), for example, subdimensional topologies can be characterized by nontrivial planes, having general topological invariants that coexist with Weyl nodes away from these planes. As a result, such phases have 3D stable characteristics such as Weyl nodes, Fermi arcs and edge states that can be systematically predicted by subdimensional analysis. Within this work we further elaborate on these concepts. We present refined representation counting schemes and address distinctive bulk-boundary effects, that include momentum depended (higher order) edge states that have a signature dependence on the perpendicular momentum. As such, we hope that these insights might spur on new activities to further deepen the understanding of these unexplored phases.