Topological Classification of One-Dimensional Chiral Symmetric Interfaces

TL;DR

This paper develops a topological classification scheme for one-dimensional chiral symmetric interfaces on a 2D substrate, emphasizing the importance of substrate entanglement and Green's function analysis for accurate topological characterization.

Contribution

It provides a rigorous proof of topological classification validity via Green's functions and highlights the necessity of considering substrate entanglement in topological indices.

Findings

Green's function-based classification is valid for these interfaces.

Entanglement with the substrate affects the topological index.

Incorrect handling of the ground state projector leads to errors.

Abstract

We address the topological classification of one-dimensional chiral symmetric interfaces embedded into a two-dimensional substrate. A proof of the validity of a topological classification based on the Green's function by explicit evaluation of the topological invariant is presented. Further, we show that due to entanglement between the in-gap modes and the substrate, the full physics of the substrate that is contained in the Green's function is required. This is done by considering a classification scheme derived from the reduced ground state projector, for which we show that an uncritical handling produces erroneous changes in the topological index due to entanglement driven gap closures. We illustrate our results by applying them to a tight-binding model of a spiral magnetic interface in a s-wave superconductor.