Superconducting Quantum Circuit Simulator Of High-order Topology In Breathing Kagomé Lattice And Its Extention

In the past decades,studying the topological band properties of matter has been one of the hot issues in condensed matter physic.Recently,a new type of topological phase,higherorder topological insulator,has attracted much attention in theory and experiment because of its singular body-edge correspondence.However,the physical models of some higherorder topological insulators have severe requirements for the hopping coefficients between lattice points,which makes it difficult to be physically realized in conventional electronic materials.In view of this difficulty,we propose a higher-order topological quantum simulation based on the physical system of superconducting quantum circuits.Quantum simulation is the use of controlled artificial quantum systems to simulate a number of widely concerned physical systems.With the increasing maturity of various artificial quantum system manipulation techniques,quantum simulation is considered to be a powerful way to explore quantum multibody problems.Based on the current microelectronic integrated circuit technology,superconducting quantum circuits have great advantages in design,control and integration.These advantages enable superconducting quantum circuits to extend the range of simulated parameters to areas difficult to reach in conventional condensed matter physical experiments,which is considered to be one of the most promising physical platforms for effective simulation of several multibody physics.Hence,in this paper we explore the use of superconducting quantum circuits to simulate several higherorder topological properties of respiratory kagomé lattices,our main results include:Firstly,we propose a theoretical scheme for respiratory kagomé lattice in superconducting quantum circuit.For this scheme,the lattice point of the breathing kagomé lattice is realized by using a superconducting transmissionline resonator(TLR),which is connected together by a superconducting quantum interference device(SQUID)grounded at one end,and the coupling between the cavities is induced by parametric modulation.This makes the hopping intensity and phase between lattice points adjustable one by one.Compared with conventional electronic systems,this tunability can not only bring unparalleled advantages to the simulation of high-order topological insulators,but also further facilitate the introduction of strong magnetic field,disorder,interaction and other mechanisms.Further,we develop the advantages of superconducting quantum circuits in tunability.Taking advantage of the adjustable phase of the coupling strength between the lattice points,we add a controllable magnetic field to the breathing kagomé lattice to observe the topological phase transition of the system under the competition of the magnetic field and the lattice transitions;In order to observe the increase and decrease of angular mode caused by the change of edge morphology,the lattice points are increased or decreased effectively on the lattice edge by the advantage of adjustable hopping coefficient between lattice points;At the same time,the next-neighbor hopping is added to the lattice point to explore the robust properties of angular modes under chiral symmetry protection.we propose that the higher-order topological properties of the system in the above various cases can be verified by the observation of corner states.Thus,we propose a scheme to measure the corner states in the breathing kagomé lattice.The principle of this scheme is that the steady states of the lattice can exhibit several higher-order topological properties of the corner states through the interaction of photons with proper pumping and dissipation.The advantage of this measurement scheme is that not only the coherence of the system is low,but also the steadystates photon number of a single or a few lattice points can be detected to obtain the frequency and spatial distribution of the photon corner.Finally,we further promote the ideas and methods mentioned above.By using the integration of superconducting quantum circuits,we propose to apply the idea of square root to the simulation of higher-order topological insulators by superconducting quantum circuits to discuss the realization scheme and related properties of kagomé-graphene lattice.We find that the kagomé-graphene lattice is very different from the respiratory kagomélattice under the joint action of pumping and dissipation of photons,which is mainly shown as positive and negative angular modes with E=0 as symmetry point pair.Controllable addition of strong magnetic field in kagomé-graphene lattice does not have a substantial effect on the higher-order topological properties.However,when the or decreasing the number of lattice points,the number of angular modes will increase and decrease.