Topological Corner States Realization Of 2D Honeycomb Non-reciprocal Circuit

In past decades,the topological states of matter is one of the most important topics in condensed matter physics.Topological insulator,different from the traditional insulator,is a special system with internal insulation and conductive properties at the edge.In recent years,emerging topological states have been successively realized in various classical systems.The topological states are symmetry-protected and robust to the defects and perturbations,which has potential application value in the future science and technology industry.However,studies on the topological states have been mostly implemented in closed Hermitian systems.Recently,it has been found that in open non-Hermitian systems,the topological properties of matter are closely linked with the open boundary,and the traditional bulk-edge correspondence cannot be used directly for the description of nonHermitian topological properties.Thus,new concepts such as the non-Bloch theory,the generalized Brillouin zone have been proposed.Non-Hermitian skin effects naturelly exist in non-Hermitian systems,where the distribution of states in the system tends to a certain boundary.Therefore,it is also important to study the competitive relationship between topological states and skin effect.Topolectrical circuits build a bridge between electronic engineering and topological physics.The inductive-capacitor(LC)resonant circuit as the basic unit can simulate the lattice point and unit cell in crystal lattice systems.Therefore,the circuit system becomes an important platform for studying the topological properties of matter.In the thesis,we investigate non-Hermitian topological properties in a two-dimensional honeycomb system and explore the competitive relationship between non-Hermitian topological states and non-Hermitian skin effects.Theoretically,a two-dimensional nonreciprocal honeycomb system is constructed and a nonreciprocal coupling between the lattice nodes is introduced to form a non-Hermitian system.Then,by using the similarity transformation,the generalized Brillouin zone is defined to study the band characteristics of the system.Based on the generalized Brillouin zone,the non-Bloch topological invariant,non-Bloch winding number and non-Bloch berry phase are defined to study the topological phase transition of the system.Finally,by calculating the topological corner states of the system,we study the competitive relationship between the corner states and non-Hermitian skin effect,that is,the topological corner state is gradually dragged by the skin effect with the non-reciprocal parameter,and the locality of the corner states decays exponentially with the increase of the non-reciprocal parameter.Experimentally,we design and print a 70-nodes-lattice rhombus honeycomb circuit board.Topological corner states are detected by measuring the voltage distribution.At the resonance frequencies,the presence of topological corner states is observed at the two sharp angles of the rhombus system.The skin effect of the system moves the distribution of states toward the right boundary,so we experimentally detect that the intensity of the left corner state decays exponentially with the non-reciprocal parameter.The experimental observations correspond with theoretical calculations.The study provides important theoretical support and experimental basis for the understanding of the topological properties of non-Hermitian systems.It provides an reference for non-Hermitian physical topology in other classical systems,such as solid,photon and phonon systems.