The Higher-order Topological State Of Honeycomb Topological Circuit

In 2017,Benalcazar found that the corner charge is quantized in a specific kind of tetragonal crystal,and this kind of system is named as quadrupole insulator.The topological states of quadrupole insulator are localized at the corner,which does not meet the "bulk-edge" correspondence of topological insulator.To describe this kind of new topological states,the concept of higher-order topological insulator is proposed.In recent years,higher-order topological insulator is a research focus in condensed matter physics.According to the " bulk-edge " correspondence,the topological states in the topological insulator are only one dimension lower than that of the sample,while the topological states in the higher-order topological insulator are two or more dimensions lower than that of the sample.At present,the higher-order topological states have been extended to a variety of systems,including electronic system,mechanical and acoustic system,microwave system,optical system,circuit system and so on.The circuit system has nice operability,strong reliability and low cost,which is an ideal platform for exploring the properties of high-order topological states with experiments.In terms of lattice types,including cubic lattice,kagome lattice,honeycomb lattice and so on.There are more researches and experiments on cubic lattice and kagome lattice,but less researches on honeycomb lattice.Since the higher-order topological states in the honeycomb lattice have not been observed in the circuit system,this paper constructs a honeycomb topological circuit to observe the higher-order topological states in the honeycomb lattice.The main research contents are as follows:(1)The Hamiltonian of optical waveguide array with honeycomb structure is derived,and the corresponding honeycomb topological circuit is designed.The higherorder topological states in the honeycomb lattice are observed for the first time in the circuit system,which provides a theoretical and experimental basis for the further study of the honeycomb topological circuit.(2)The simulation of the honeycomb topological circuit is carried out in LTSpice.Through the simulation,the transmission process from the beginning until the steady state of the voltage signal in the topological circuit can be obtained,thus provides a reference for studying the time-dependent evolution of higher-order topological states in topological circuits.By comparing the LTSpice simulation results with the numerical calculation results and the experimental results,the reliability of the numerical calculation and the experiment is verified.(3)If the ideal component model is used in the numerical calculation,the calculated voltage and impedance will diverge.In order to solve this problem,the loss of components is considered and the actual component model is introduced.(4)At present,most of the experiments on topological circuit observe the topological states through impedance,but in the practical application of circuit system,measuring impedance is far more difficult than measuring voltage,therefore the method of observing the topological states in the topological circuit through voltage is proposed,and the formal solution and derivation process are given.