Observing the nodal-line conversion determined by the relative homotopy

TL;DR

This paper introduces a method using temporal topolectrical circuits to identify non-Abelian nodal-line semimetals by analyzing their topological properties and nodal configurations, which are difficult to detect directly.

Contribution

The study develops a novel TTC-based approach to determine the conversion rules of nodal lines and demonstrates the emergence of NASM with unique non-Abelian nodal configurations.

Findings

Demonstrated the relative homotopy group of two-band models using TTC.

Showed how additional bands lead to the emergence of NASM.

Identified the earring nodal lines as a non-Abelian constrained configuration.

Abstract

Directly identifying the non-Abelian nodal-line semimetals (NASM) is quite challenging because nodal-line semimetals typically do not possess topologically protected boundary modes. Here, by reconstructing the correspondence between the bulk states of Hermitian systems and circuit voltage modes through gauge scale potential, the temporal topolectrical circuits (TTC) for evidencing NASM are proposed. Following the logical progress of discovering NASM, we start by demonstrating the relative homotopy group of two-band models using TTC, which can faithfully determine the conversion rules between the nodes in and out of the non-local-symmetry invariant subspace. Next, we show that those rules dramatically change with the consideration of the additional band, historically leading to the arising of the NASM. Also, we demonstrate the unique non-Abelian constrained nodal configuration -- earring nodal lines. Our results established NASM for further investigating topological line degeneracies, and proposed TTC will be a versatile platform for exploring nodal-line semimetals.