Topological Euler insulators and their electric circuit realization
Motohiko Ezawa
Abstract
The Euler number is a topological number recently debuted in the topological physics. It is defined for a set of bands unlike the Chern number defined for a single band. We propose a simple model realizing the topological Euler insulator. 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.
Topics & Concepts
Topology (electrical circuits)Topological insulatorEuler's formulaRealization (probability)Euler number (physics)Electronic circuitPhysicsMathematicsEuler equationsSemi-implicit Euler methodQuantum mechanicsMathematical analysisBackward Euler methodCombinatoricsStatisticsTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsNoncommutative and Quantum Gravity Theories