Topological Euler insulators

TL;DR

This paper introduces the topological Euler insulator, a new phase characterized by the Euler number, demonstrating its properties, edge states, and potential realization in electric circuits.

Contribution

It presents the first simple model of a topological Euler insulator, linking the Euler number to the Pontryagin number and proposing a circuit implementation.

Findings

Euler number linked to Pontryagin number in a three-band model

Presence of topological edge states when Euler number is nonzero

Impedance resonances signal topological edge states in circuits

Abstract

The Euler number is a new topological number recently debuted in the topological physics. Unlike the Chern number defined for a band, it is defined for interbands. We propose a simple model realizing the topological Euler insulator for the first time. We utilize the fact that the Euler number in a three-band model in two dimensions is reduced to the Pontryagin number. A skyrmion structure appears in momentum phase, yielding a nontrivial Euler number. Topological edge states emerge when the Euler number is nonzero. We discuss how to realize this model in electric circuits. We show that topological edge states are well signaled by impedance resonances.