Subdimensional topologies, indicators and higher order phases

TL;DR

This paper explores sub-dimensional topological phases that exhibit stable or fragile topologies within lower-dimensional spaces, revealing observable 3D features like Weyl nodes and Fermi arcs through sub-dimensional analysis.

Contribution

It introduces refined classification schemes and analyzes bulk-boundary effects of sub-dimensional topologies, advancing understanding of these previously unexplored phases.

Findings

Sub-dimensional topologies can produce observable 3D features.

Refined representation counting schemes are developed.

Momentum-dependent higher order edge states are characterized.

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 {\it sub-dimensional topology}. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within sub-dimensional 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, sub-dimensional topologies can be characterized by non-trivial planes, having general topological invariants, that are compensated by 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 sub-dimensional 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.