Study Of Photon-assisted Dirac Electron Fano Resonant Tunneling

Fano resonance(FR),a quantum phenomenon that arises from the quantum interference between the continuum and the bound states,with the anomalous asymmetric line shapes are different from the conventional symmetric resonance.As a fundamental phenomenon,FR has been observed in many physical fields.It is well known that the low-energy band structure of graphene is gapless and linear near the Fermi energy,and the dynamics of the low-energy electrons can be governed by the 2D massless Dirac equation.In this thesis,we investigate the photon-assisted Fano-type resonance transmission of Dirac electron through a time-periodic potential in graphene by analytical and numerical method.The paper is organized as follows four parts:In Section I,we first introduce the properties of two-dimensional graphene materials and the characteristics of the electron band,and review the photon-assisted electon transport,mainly including the research progress of photon-assisted electron tunneling in the traditional semiconductor heterojunction quantum well and the graphene quantum well.Then,the concept of the Fano resonance effect and the theoretical tools which are used in the study of electronic transport,such as the Floquet theorem,the scattering matrix(S matrix)and the transmission matrix,are introduced.In Section ?,the massless Dirac electron tunneling through a time-periodic double-well potential is investigated.The previous theoretical works have found that when the periodic oscillatory field is added to the electrostatic potential of graphene,there will be Fano type resonance generated by Dirac electron tunneling.Our work is to extend the single well potential structure to a double well potential structure.By using the Floquet scattering theory and the scattering matrix method,the photon-assisted resonant tunneling of the Dirac electron in the double well potential of graphene is studied.Different from the single quantum well structure,in the double quantum well structure,since the resonance tunneling through a thin barrier between two wells leads to the level splitting of bound states,the Fano-type resonance spectra through double wells are divided into two asymmetric resonance peaks.Meanwhile,it is found that the relative phase of the two oscillating fields can adjust the line shapes of the asymmetry Fano-type resonance peaks.Additionally,the numerical calculation results show that the profile of Fano-type resonance can be also controlled by adjusting the frequency and amplitude of the applied oscillating fields,and the structure of the static quantum wells.In Section III,the massive Dirac electron tunneling through a time-periodic potential with magnetic field modulation is investigated.Experiments have demonstrated that an energy gap is opened by epitaxially growing graphene on a substrate.The induced gap is caused by breaking the equivalence between the A and B sublattices and lifting the degeneracy of the valence and conduction bands at the Dirac points.This induced gaps lead to a finite mass for its charge carriers,which are obedient to the massive Dirac equation.Based on the Floquet scattering theory,we use the scattering matrix method to calculate the conductance of a mass Dirac electron through a time-dependent periodic single well under magnetic field modulation.The results show that when the external periodic oscillating field is a low frequency one,the magnetic field will change the energy level structure of the bound state of the potential.well and induce the generation of multiple Fano resonant peaks.Under high frequency oscillation field,there will be multiple Fano resonance peaks both in the presence and absence of magnetic field.The only difference is that the external magnetic field changes the mechanism of Fano resonance peak.Meanwhile,the magnetic field suppresses the new Fano type resonance peak.In addition,we also find that the intensity of the oscillating field would affect the interference intensity of the incoming Dirac electron and the potential well,and lead to the change of the profile of Fano-type resonance.Finally,a summary of our work is given.