Generalized Topological Characteristics In A Trimerized Non-Hermitian Lattice

Topological insulators are a new type of material discovered in recent years,and research in the field of quantum optics is now very active.A topological insulator is the intersection of a conductor and an insulator.Its bulk state is an insulator and cannot be electrically conductive,but its surface state or edge state is a metallic state that can participate in conduction.These interface states reverse the symmetry protection by hand,without being affected by impurities and disorder,as described by the massless Dirac equation.Topological insulators are also closely related to recent research hotspots such as quantum Hall effect and quantum spin Hall effect.The basic characteristics are to use the topological properties of electron energy bands in materials to achieve various novel physical properties.In this paper,we mainly study a series of novel topological properties brought about by one-dimensional trimerization in non-Hermitian lattices.First,in order to introduce a next-nearest neighbor coupling in a trimerization system,the one-dimensional linear structure design is improved to a one-dimensional zigzag structure in which each unit cell is designed as a closed triangle.Through the extended non-Hermitian trimerization model,the energy spectrum band under the influence of the next-nearest neighbor coupling produces new evolution characteristics.The results show that the energy spectrum consists of three bands,and the band contains the upper and lower bands.When the next-nearest neighbor coupling coefficient increases from zero,the upper and lower energy gaps and edge states begin to produce opposite changes.At this time,the real and imaginary parts of the energy spectrum are only symmetric about ?=?,and are no longer symmetric about E= 0.And the upper energy gap at the center begins to shrink,and the lower energy gap begins to expand.This in turn leads to a reduction in the topological nontrivial regions containing the upper edge states and an increase in the nontrivial regions containing the lower edge states.Therefore,influenced by the special properties above,we can get a control transition about the number of edge states between 0 and 4.At the same time,based on the zigzag trimerization model structure,we introduce a synthetic gauge field into the system to create a magnetic flux in the unit cell,producing a Peierls5 phase with new topological features.Secondly,based on the extended trimerization model,we introduce the different values forward and reverse of the nearest-neighbor coupling coefficient of the system,and discuss the skin effect of the trimerization lattice system.Different from the dimerization SSH model,in the extended trimerization lattice,due to its unique energy band characteristics,the system achieves the purpose of controlling the number of degenerate topological edge states.In this system,the degeneracy and symmetry of the edge state are destroyed,that is,as the nearest-neighbor coupling forward and reverse difference increases,although the bulk energy spectrum still maintains the original symmetry,the upper and lower edge state energy bands symmetrical changes occur.Specifically,in the real part of the edge energy band,the length of a pair of edge states respectively distributed in the upper and lower energy gaps is constant,and remains symmetric.The other pair of edge states begin to shorten at the same time,and are still symmetrical;however,in the imaginary part of the edge state,the two degenerate edge states of Im(E)= 0.1 remain unchanged,and the two correspondences of In(E)=-0.1 The edge state of the real part begins to shorten and eventually degenerates into a bulk state.In the future,by designing a variety of multi-polymerized non-Hermi lattices and applying them to the study of topological quantum materials,more meaningful and novel topological physical properties will be discovered.