Effect Of Interaction Between Fermion And Boson On The Electronic State

Recently, a series of2-d or quasi2-d system material was discovered with peo-ple’s efforts and the improvement of technology. The researches on various properties of these materials attracted people’s more attention. In these materials, various prop-erties of electron was researched vastly. In addition to the interaction of electronic-electronic, the coupling between electron and boson has more effect on properties of electron in many case. So we have done some work about three2-d materials by consid-ering coupling of between electrons and bosons. They are "electron-phonon coupling research at surface of graphene ","research about Multiphonon effects at the surface of metals","research about Renormalization of spin polarized itinerant electron bands in the normal state of a model ferromagnetic superconductor"First, because of coexistence of superconductivity with ferromagnetism found in UGe2and other compounds has attracted much attentions, at the turn of the century. Suhl proposed a model for coexisting ferromagnetism and superconductivity and shown a theory with ferromagnetic ordering based on localized spins, the exchange interaction J between conduction electrons and localized spin is taken as the pairing glue for s-wave superconductivity. In our thesis, we study the normal state properties of itinerant electrons basing on a model that was obtained by extending suhl model a model and combining Heisenberg model. We adopted tight binding approximation to the system before considering interac-tion between electron and localized spins. However, we obtained a model with electron-magnon scattering by adding a weak ferromagnetic Heisenberg term-JHSi·Sj to the model proposed by Suhl and considering the excitation of spin-wave of long range ferromagnetic order.We show that this J term will firstly renormalize the normal state single conduc-tion electron structures substantially. We find dramatically enhanced or suppressed magnetization of itinerant electrons for positive or negative J. Singlet Cooper pair-ing can be ruled out due to strong spin polarization in the J>0case while a narrow window for s-wave superconductivity is opened around some ferromagnetic J.In second part we study the relation between renormalization of the chemical po-tential due to multiphonon effects at the surface of metals and doping by solving the strong-coupling self-consistent equations of a two-dimensional(2D) electron-phonon interaction system. We present the quasiparticle dispersions and inverse lifetimes of a2D electron systems interacting with Einstein phonons under the different dopings (corresponding to chemical potentials). We find that the effect of electron-phonon in-teraction on electron structure is strongest at the half filling, but it has no effect on the chemical potential. However, the chemical potential shows distinct renormalization effects away from half filling due to the electron-phonon interaction.In last part, our work is electron-phonon coupling research at surface of graphene. Because in last few years, there are some experiments work about the emerging mate-rial graphene, which is interesting for people.One of these is Angle distinguish photo-electron spectrum experiment about electronic properties and attract people’s attention. The study found that the actual dispersion have not be consistent with classic theory. Although, the dispersion near the point K is linear, there is kink structure near0.2ev under the Fermi energy. For explaining the phenomenon, people considered electron-phonon coupling effect. But they adopted analytical method to do it. Our work basis on their work, and adopted green function method to studied electric phonon strong cou-pling model. Then we calculate the modifications of electron line which is caused by the coupling between Einstein LO phonon mode and electron. And we obtained elec-tron self-energy, spectrum function, and dispersion under the action of electron-phonon coupling. We got the results is consistent with that of the experiment.