Quantum Pumping With Adiabatically Modulated Barriers In Three-band Pseudospin-1 Dirac–weyl Systems

In this paper,we mainly study the transport properties of the quantum pumping with adiabatically modulated barriers in three-band pseudospin-1 Dirac-Weyl systems and in graphene.Generally,the classical pump refers to the phenomenon that the material in the system transfers the material flow from low potential energy to high potential energy by absorbing energy from outside the system.However in mesoscopic system,the physical process of DC current and voltage generated by nano devices by adjusting some parameters of the system periodically with time is called quantum pumping,even without any bias source.The influence of different material structure on the pump current is very significant.The pseudospin-1 Dirac-Weyl system is a relatively new system,which is of great physical significance for its study.Based on the scattering matrix theory and adiabatic scattering theory,this paper studies the relationship between the transmission probability and the incident angle in the two barrier structure of the pseudospin-1 Dirac-Weyl systems and graphene,we find that the transmission probability is very different from that of ordinary materials.When the barrier is high,the transmission probability is small of double barrier structure in common materials,when the barrier is low,the transmission probability is large,and resonance tunneling occurs at a certain energy value,but in the double barrier structure of the pseudospin-1 Dirac-Weyl system and graphene,because of the particularity of the dispersion relation of the system in the low energy state,when the incident angle is small,the higher the barrier,the greater the transmission probability of the system,or even the complete tunneling.Moreover,the complete tunneling does not correspond to a specific value but a continuous range,which is Klein tunneling.The numerical results show that the pump current in this structure is also specific.It is found that in graphene,when the barrier height is higher than the Fermi energy range,the forward current and the reverse current will appear simultaneously,while in the lower Fermi energy range,only the forward current will appear.In the pseudospin-1Dirac-Weyl system,it is found that in some larger Fermi energy range,the pump DC current flows in the same direction at any incident angle,resulting in sharp negative angle average pump current below the Dirac point,sharp positive angle average pump current above the Dirac point,and its angular average pump current at the Dirac point The point will not diverge.This is not possible in ordinary materials.This phenomenon is due to the Klein tunneling effect caused by the particularity of the system.At the same time,we also calculatethe numerical results of berry curvature function,which is related to the current expression,and use the results to explain and analyze the magnitude and direction of the pump current,at the same time,the consistency between the Turnstile Model and the Berry Phase Treatment.