Investigations Of The Goos-h(?)nchen Effect In Low-dimensional Materials Under Photoelectric Control

It is an important research direction for electron beams to simulate optical-like behaviors of beams.At the same time,they are also widely used,especially in the application of ultralarge-scale integration and advanced information technology,which provides great potential for the development of fundamental quantum physics and electronic devices.Since the advent of graphene,the control of graphene by external fields has become the focus of research,resulting in a new field of research,namely,electron transport in low-dimensional materials.In addition,other two-dimensional materials have been discovered successively,especially silicene and similar two-dimensional(2D)materials composed of group iv elements.Studies have shown that by applying an external electric field or a circularly polarized light field,a wide variety of band gap modulations can be generated.In the past few years,the academia has carried out a series of theoretical and experimental studies on the Goos-H(?)nchen effect in low-dimensional materials.Based on this,this paper proposes two models for the Goos-H(?)nchen effect of low-dimensional materials controlled by circularly polarized light fields.One is a silicene junction model based on photoelectric regulation,and the other is a graphene junction model based on optical field regulation.The main research contents are as follows:(1)The effects of the circularly polarized light field and the external vertical electric field on the band structure of silicene and the spin-and valley-polarization-dependent Goos-H(?)nchen shifts of transmitted electrons are investigated in detail.The results show that the Goos-H(?)nchen shift of silicene resulting from the external perpendicular electric field does not have the characteristics of spin or valley polarization,while that from circularly polarized light or the exchange field is spin-polarized.More importantly,the combined effect of the external perpendicular electric field and the exchange field or circularly polarized light can cause the Goos-H(?)nchen shift of the system to be spin and valley polarized.It is particularly worth noting that when the three modulations are considered at the same time,as the exchange field changes,the system will have a positive or negative Goos-H(?)nchen shift.Furthermore,by appropriately controlling the strengths of these three fields,the spin-polarized and valley-polarized features of the shift are more pronounced.The magnitude of the shift can also be changed by adjusting the angle of incidence.We hope our findings can be helpful for the electrical control of spin and valley filtering and the application of quantum information.(2)Taking the graphene junction as the research model,the band structure and the Goos-H(?)nchen shift of transmitted electrons under the modulation of the circularly polarized light field,the exchange field and the mass term are systematically studied.It was found that when circularly polarized light is applied in the mass graphene,a valley band gap can appear,and the Goos-H(?)nchen shift exhibits valley-related features.When an exchange field is applied in the mass graphene,a spin band gap can appear,and a spin-dependent Goos-H(?)nchen shift occurs.Furthermore,the spin band gap and the valley band gap and the spin and valley polarization related Goos-H(?)nchen shift can be achieved with the combination of the circularly polarized light and exchange field in mass graphene.In addiction,by controlling the intensity of the circularly polarized light and the exchange field,the mass graphene exhibits positive or negative Goos-H(?)nchen shift.The locations where these Goos-H(?)nchen shifts appear is closely related to the band structure.We hope that our work will be more conducive for future applications in graphene polarization transport devices.