Pinch-point spectral singularity from the interference of topological loop states

TL;DR

This paper reveals how pinch-point spectral singularities in flat band systems originate from interference among topological loop states, providing a new perspective on their topological and spectral properties.

Contribution

It establishes a mathematical relationship between compact localized states and non-contractible loop states, linking spectral singularities to topological interference patterns.

Findings

Pinch points are interpreted as interference among topological loop states.

A mathematical relationship between CLS and NLS is derived.

The approach enables extraction of topological information from spectral features.

Abstract

Pinch point is a spectral discontinuity found in the neutron diffraction image of spin ice. Similar spectral singularity is commonly observed in a broad range of systems that have a close connection with flat bands. We focus on the electron flat band and its two topologically distinct classes of wavefunction: the compact localized state (CLS), and the non-contractible loop state (NLS). We establish their simple mathematical relationship, showing that different Bloch NLSs can be derived as momentum derivatives of a Bloch CLS, depending on the approaching direction toward the singular point. This CLS-NLS correspondence helps visualize the pinch point as an interference pattern among NLSs through a ``polarizer", which encodes the information about the location of singular momentum and the experimental techniques like spin-polarized photoemission spectroscopy. It helps extract topological information knit to microscopic electronic and magnetic structures.