Fano Effect In Coupled Quantum Dot Structures

A semiconductor quantum dot (QD) is a quasi-zero-dimensional mesoscopic structure, which presents discrete electron energy spectrum and strong electron interaction. Because of such characteristics, a single QD is viewed as an artificial atom. When several quantum dots locate closely to each other, electron can tunnel from one QD to another, which gives rise to the QDs coupled to each other. Then we can call this system an artificial molecule. In contrast to a single QD, multiple QD structures possess more structure parameters that can be used to change their electronic transport properties. Therefore, the investigation on the multiple QD structures is the highlight in the field relevant to QD systems.We know that quantum interference plays a dominant role in the process of electron tunneling through a mesoscopic structure. Fano effect is a typical quantum interference phenomenon, and its essential is the interference between the resonant and nonresonant processes. As a result, asymmetric line shapes occur in the electron transport spectra in the coupled QD structures. It can't be denied that the dephasing effects can play a distinct role in the process of electron tunneling through the QD structures. So it is interesting to investigate the Fano lineshapes with the dephasing effects. In addition, there are a lot of decoherence mechanisms, such as the electron-electron interaction and electron-phonon (e-p) interactions. Then, we studied what changes have taken place in the Fano effect with decoherence mechanisms. Below we outline our works briefly. In this thesis, by means of non-equilibrium Green function technique we report our theoretical investigations about the Fano affect in several typical multiple QD structures and obtain some meaningful results.Firstly, we have theoretically investigated the electronic tranport properties in the ferromagnet-double QDs-ferromagnet structure. By modulating the coupling parameters of QDs appropriately, the Fano resonance occurs. Then we investigate the effect of spin polarization on the Fano resonance in the whole system. Due to the introduction of spin polarized current, the original electronic transport properties in the coupled QD system change. To be specific, when the polarized directions of the two electrodes are parallel or anti-parallel, the height and width of Fano resonance peaks are modulated. It is also found that the conductance peak is suppressed when the electrodes are polarized. When the polarized directions are collinear with a large polarizability, it is seen that in the original conductance the resonant peaks transformed into antiresonance valley. In addition, when the polarized directions of electrodes are modulated in three dimensions, we find the periodical law of the change of conductance with every azimuth angle. Furthermore, we find that the influence of the angleφon the conductance is limited. Then, we express the transmission paths of the electron that take part in the tunneling process in the whole system, with the Feynman path language. It is should be noticed that the destruction of Fano interference originates from the summation of infinite order Feynman paths. Then, we studied the effect of Rashba spin-orbit (SO) coupling interaction on Fano interference in such QD structure. It is found that the Rashba interaction brings about a spin-flip interdot hopping term. As a result, the antiresonance of conductance disappears. Moreover, the QD levels, the eigenenergies of the double-QD molecule, and the couplings between the eigenstates and leads can be adjusted by the Rashba SO coupling. Therefore,the Fano peak moves and the asymmetric Fano lineshape is destroyed.Secondly, we have investigated the effect of e-p interaction on the Fano lineshape in the linear conductance spectrum in the parallel double QD structure. We derive an expression about linear conductance in the presence of e-p interaction. And we find that the inelastic conductance vanishes in the zero bias and zero temperature case. We consider the local and nonlocal phonon modes on an equal footing. Both phonon modes are typical in most QD structures. But they influence the Fano lineshape of the linear conductance spectrum distinctly: The nonlocal phonon can give rise to the multiple Fano peaks, since it can provide inter-dot electron tunneling path; conversely, the local phonons mainly shift the single Fano lineshape without destroying its profile. For the case of finite temperature, these properties are kept though the complex inelastic scattering process.Thirdly, we studied the electronic transport through the parallel coupled QDs. The different Fano line-shapes occur when the strength of QDs-leads coupling and magnetic field are modulated appropriately. By transforming the Hamiltonian into its molecular representation, we obtain the conditions of decoupling between the quantum states and the leads.Finally, by virtue of the parallel coupled double QD structure, the Fano effect is investigated in the presence of the many-body interaction, including the intradot and interdot electron interactions. It is found that both the intradot and interdot Coulomb repulsion result in the appearance of multiple energy levels, which lead to the complicated quantum interference. To be specific, only the intradot electron interaction being considered, the Fano resonance is not destroyed. And there exist two types of Fano lineshapes. However, the Fano effect is destroyed remarkably with the increase of the interdot Coulomb interactions.