Topological Euler insulators

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.

4 pages, 6 pages

References in corpus (3)

• Topological Euler class as a dynamical observable in optical lattices
• Geometric approach to fragile topology beyond symmetry indicators
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization

Cited by in corpus (12)

• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Non-Abelian tensor Berry connections in multi-band topological systems
• Quantum Valley Hall effect without Berry curvature
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Euler band topology in superfluids and superconductors
• Hinge modes of three-dimensional Euler insulators
• Three-dimensional spinless Euler insulators with rotational symmetry