Construction And Phase Transition Of High-order Topological Phase

In recent years,topological insulator have made remarkable progress in theory,materials,preparation methods and new applications,and become a research hotspot.The discussion on the construction and phase transition of high-order topological phase in topological insulator is not only helpful to understand its theory,but also can promote the development of practical applications.However,little research has been conducted on how to control the local position of topological phases.Realizing phase transitions of different topological phases and edge states of armchair shapes is also a hot topic.This study proposes an innovative method that utilizes lattice even-odd effects to control the local position of higher-order zero-energy topological phases in the one-dimensional Aubry-Andr\é-Harper model(AAH model),and conducts theoretical and experimental predictions on the corner states of topological zero-energy.This zero-energy corner state cannot form a continuous state in a continuum,so it can be directly observed through experiments.The control of the position and number of zero-energy corner states can be achieved by modulating the even-odd of the number of lattices without adding other additional conditions,so it has the advantage of simplicity.This study provides new ideas for constructing zero-energy corner states in the future and is expected to be widely applied in the field of physical technology.This study further analyzes how to achieve topological phase transition and proposes an effective method for constructing localized states in graphene quantum dots using uniaxial strain effect.We have successfully achieved the historically difficult armchair edge state and conducted theoretical verification through numerical simulation.The distribution characteristics of local states are closely related to the hopping amplitude caused by uniaxial strain direction.After applying uniaxial strain,graphene quantum dots can be seen as an extended two-dimensional Su-Schrieffer-Heeger(SSH)model.In order to analyze local states,we innovatively propose a method of establishing a two-dimensional extended SSH model using one-dimensional SSH chains.This method predicts that the occurrence of localized states is highly consistent with the simulated localized states caused by uniaxial strain on monolayer graphene.It should be emphasized that the formation of these local states only requires strain,and they are all in the band gap of the system,so they can be easily observed directly and used as single channel Quantum wire.This theoretical analysis method is not only applicable to solid crystals such as graphene,but also to intraocular lens,such as photonic crystals and acoustic crystals.This discovery provides a new approach for circuit design in quantum computing.