Embedded Topological Insulators

TL;DR

This paper generalizes free fermionic topological insulators to include embedded subsystems of different dimensions, revealing new topological phenomena at defects within trivial insulators.

Contribution

It introduces a classification method for embedded topological insulators and demonstrates their physical effects at crystalline defects.

Findings

Embedded topological insulators can host novel edge modes at stacking faults.

Periodic embedding induces topologically non-trivial phenomena in trivial systems.

Examples span various dimensions and symmetry classes.

Abstract

We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a trivial insulating environment. A general procedure is described to isolate and classify such embedded topological insulators and we present three representative examples in varying dimensions and symmetry classes. Moreover, we demonstrate with concrete examples that the presence of periodically embedded topological insulators in an otherwise trivially classified system can lead to topologically non-trivial physical phenomena on crystalline defects; namely, novel topological surface/edge modes at stacking faults and partial edge dislocations.