Photon-assisted Dirac Electron Quantum Transport

The characters of the topological insulator are completely different of traditional "metal" and "insulator", it is a new type of quantum states of matter. This special matter states have a bulk energy gap and surface states is gapless, so topological insulator behaves as an insulator in its interior but whose surface contains conducting states. The surface states are protected by time-reversal symmetry. Electrons on the surface of a topological insulator obey the massless Dirac equation, rather than the traditional Schrodinger equation which leads to the different properties of the transport on the surface of topological insulator. In this thesis, we construct the nanostructures on the surface of topological insulator using electric and magnetic potential and give the wave functions in every regions based on the massless Dirac equation and Floquet theory. The boundary continuity of the wave function is used to obtain the scattering matrix, which can give the transmission coefficient of the electrons through the nanostructures. Moreover, we also discuss the effects of system parameters on the electron transmission. The main contents are as follow.(l)The photon-assisted quantum transport of Dirac electron through the time-dependent periodic potential and magnetic field modulation. When there is no oscillating field in the region of potential well, Dirac electron exhibits resonance transmission through the potential region like Schrodinger electrons. When an oscillating field is added, the quantum interference between the bound states and continuum states due to the interaction of electron with oscillating field can result in the occurrence of asymmetric Fano-type resonance in transmission spectrum. The resonance position is related to the parameters of the potential well and the oscillating frequency. When an external magnetic field is applied in the potential region, the effective depth of the potential well is changed, with the magnetic field increasing the resonance transmission spectrum and Fano resonance peaks shift to the direction of higher energy.(2)When an external magnetic field is applied outside the potential well, The effects of the parameters on the transmission spectrums of Dirac electron through the system is similar to the case that the magnetic field is applied in potential well. But with increasing the magnetic field outside the potential well the resonance transmission and asymmetric Fano resonance peaks shift to the direction of low energy, which is opposite to the case that the magnetic field is applied in potential well region. The increase outside potentials well, in fact, leads to decreasing of the effective depth of well and the reduction of the bound state energy.