Study On Quantum Tunneling In The Overlapping Two-dimensional Layer-structured Material

We develop a pseudo-region method to investigate the electronic transport characteristics of partially overlapped monolayer Dirac materials.To match the wave function more naturally,the pseudo-tunneling region is considered to connect the semi-infinite monolayer flake.We prove that pseudo-region method is consistent with the continuity equation of quantum mechanics.We prove that the electron will not leak to the pseudo-region by choosing proper formation and parameters of the Hamiltonian of the pseudo-region.Therefore,the quantum tunneling is still limited in the real overlapping structure,almost irrelevant to the pseudo-barrier region.For simplicity,we choose a special case of the proposed form of pseudo-region,which is called the pseudo-barrier case.By choosing proper pseudo barrier in the pseudo region,the electronic wave function is exponentially suppressed and the incident electrons are perfectly reflected in this region.Through theoretical analysis,we prove that the boundary condition derived from the pseudo-barrier model is very similar to the boundary condition of the zigzag graphene ribbon except the pseudo-spin is coupled with the parity of the translation invariant direction of the system.For AA-stacking we found two frequencies from the oscillation of transmit probability which is determined by the two independent wave modes in the overlapping region.In the low energy limit,the two frequencies approach to the two frequencies of oscillation of conductance observed in previous study.By applying a finite voltage difference on the two layers of the partially AB-stacking overlapping graphene,the conductance becomes very low about 10^-28 of the unit conductance.This result is 18orders better than the previous study which proposed a partially overlapping graphene which is different from the one in this work used to block the current as the single layer is always conductive because of Klein tunneling.By applying fermi velocity modification,we have unequal fermi velocities with respect to the two layers of the partially overlapping graphene.Snell’s law is observed as the Dirac fermion of graphene performs like photon.We proved it from theory and the numerical result is accurately coincident with the predicted critical angle.For the partially AA-stacking overlapping graphene,the conductance in the low energy region is very sensitive to modification of the fermi velocity.By slightly lowing the fermi velocity of the incident layer,the conductance of the low energy region is significantly suppressed.To sum up,to suppress the conductance of the partially AB-stacking overlapped graphene,it’s better to apply a voltage drop across the two layers of the system;to suppress the conductance of the partially AA-stacking overlapped graphene,it’s better to modify the fermi velocities of the two layers of the system.The pseudo-region method is widely applicable to the quantum tunneling or the bound state problems for more complex cases,such as overlapping junction with different monolayer materials,twisted bilayer devices,and partially overlapping semiconductor/superconductor heterostructures.