Scattering theory of delicate topological insulators

TL;DR

This paper introduces a scattering theory approach to delicate topological insulators, revealing how reflection phases can detect their unique topological features and proposing experimental implementations.

Contribution

It develops a scattering framework for delicate TIs, linking reflection phases to their topology and suggesting symmetry conditions for boundary state stability.

Findings

Reflection phase captures delicate topology via returning Thouless pump

Additional symmetries can stabilize boundary states beyond conventional methods

Proposes a photonic crystal experiment to measure reflection phase and detect topology

Abstract

We study the scattering theory of delicate topological insulators (TIs), which are novel topological phases beyond the paradigm of the tenfold way, topological quantum chemistry, and the symmetry indicator method. We demonstrate that the phase of the reflection amplitude can probe the delicate topology by capturing a characteristic feature of a delicate TI. This feature is the returning Thouless pump, where an integer number of charges are pumped forward and backward in the first and second half of the adiabatic cycle respectively. As a byproduct of our analysis we show that requiring additional symmetries can stable the boundary states of a delicate TI beyond the conventional requirement of a sharply defined surface. Furthermore, we propose a photonic crystal experiment to implement a delicate TI and measure its reflection phase which reveals the delicate topology.