Quantum Transport In Chern Insulators On M?bius Strips

Since topological insulators have been proposed theoretically,topological quantum states and topological quantum transport problems have aroused many people’s research interests.In 1988,F.M.D.Haldane added interlaced magnetic flux to two dimensional(2D)honeycomb lattice and obtained energy bands with topological properties.When the low energy band is completely filled with the integer electrons and the high energy band is not occupied,an integer quantum hall state without Landau energy level is obtained.The Topological insulator that satisfies the time reversal symmetry breaking is called the Chern insulator,and is marked by Chern number (?)= ±1.The Haldane model has been studied extensively as the original model of anomalous Hall effect,especially in the structure of graphene lattice,different geometric configurations are used to obtain new physical properties.As Chern Insulator,people are mainly limited to the calculation of physical quantities such as energy band,Chern number,state density and so on.But,there are few studies on the transport properties.However,the study of topological problems in special geometric structures has been the trend of development in recent years.Therefore,the research on the transport properties of the finite system is full of development prospects.In this paper,we construct a M?bius strip transmission system based on the Haldane model,and use the one-to-one correspondence between the conductance and the Chern number,and use more detailed physical images to understand the topological and transport properties of the system.In the study of the existing domain wall system,we found that when the wire contains domain walls,it will get the same transport effect as the high Chern number system.In order to control the transport properties of quantum devices,we have discussed in detail the M?bius strip with one and three domain walls.First,in the M?bius strip with only one domain wall,we add magnetic flux to the domain walls and find that the transition coefficients between the domain walls can induce alternately distributed edge states.In addition,for the stability of quantum devices,we explored the effect of the M?bius strip size on transport,and found that when the width of the model is greater than 11 times the lattice constant,the domain wall magnetic flux will not interfere with the conductance platform.Finally,in the systematic study of the existence of three domain wall M?bius strip,we found the relationship between the position of the leads and the number of domain walls included and the height of the Hall platform.We can arbitrarily control the height of the Hall conductance platform to achieve the same transport effect as the high Chern number system under the most basic Haldane model parameters.