Electron-phonon Coupling And Electronic Properties Of Electron-doped Graphene

Graphene has attracted a great deal of experimental and theoretical activity for its po-tential role as major future electronics material. Graphene consists of a single layer of car-bon atoms with honeycomb lattice structure. An important aspect of the charge dynamics of graphene is that it is governed by a Weyl’s equation or a Dirac equation with vanishing rest mass rather than a Schrodinger equation. This peculiar band structure of electrons in graphene predicted theoretically have been qualitatively confirmed by angle-resolved photoemission spectroscopy (ARPES) measurements. ARPES is a powerful experimental technique for probing the electronic spectral function A(k, ω) in two-dimensional crys-tals. In particular, ARPES allows studies of the interaction between electrons and lattice vibrations (electron-phonon interactions).In the ARPES measurements, a kink was observed at about200meV below the Fermi level∈F. Its relative position with respect to∈F is unchanged for different doping level of graphene. In order to explain this feature, many theories have been proposed. A theory of analytical calculation of electron-phonon interaction effects on the electronic properties of graphene was developed by the paper in the Physical Review Letters [Phys. Rev. Lett.99,236802(2007)]. They claimed that the main features of the observed ARPES spectra could be explained by the electron-phonon interaction. But their kink structure was not consistent with the experimental ARPES studies and the result from first-principle calculations of the graphene electronic spectra. In this paper, we revisit this electron-phonon interaction approach both analytically and numerically. In Chapter1, we introduce the characteristics and the basic structure of graphene, the principle and the data of ARPES experimenta, and outline our main work and the content. In chapter2, we introduce the electronic structure of graphene in tight binding model, the diagonalizable matrix of Hamiltonian. We also introduce the electron-phonon interaction Hamiltonian, and obtain the electron-phonon coupling matrix. In chapter3, we calculate the real and imaginary parts of the self-energy with the electron-phonon in-teraction. In chapter4, we calculate the mass-renormalization parameter λeff, the Fermi level renormalizations and the quasiparticle dispersions. Then, we compare our results with the ARPES experimental data and the first-principle calculations. In chapter5, we also study the relation between the renormalization of the chemical potential due to mul-tiphonon effects at the surface of Be(0001) and doping. we solve the strong-coupling self-consistent equations of a two-dimensional (2D) electron-phonon interaction system of Be(0001) numerically at some different doping levels. We present the self-energy of quasiparticle with electron-phonon interacting. Then, we calculate the quasiparticle spec-tral function, the quasiparticle dispersion. Finally, we calculate the renormalization of the chemical potential and the quasiparticle distribution function. In chapter6, we summary the total topic and look forward to the future of the study of electron-phonon interaction in graphene.The main work in this thesis are listed as follows:1. We evaluate analytically the imaginary parts of the self-energy and find the same results as the imaginary parts of the self-energy worked out in the paper as men-tioned above. However, the real parts of the self-energy we found have an extra term which does not appear in the real parts of the self-energy in the above men-tioned paper. And for the case that∈E0cannot be ignored as compared with the band cutoff, we must consider the extra term when we calculate the real parts of the self-energy. Then we calculate the energy distribution curves, the Fermi-level renormalization, the mass-renormalization parameter λeff, and the quasiparticle dispersion. Our results show that the electron-phonon interaction has a slight effect on the band-structure renormalization at lower doping level n=1.0×1013m-2. And we calculate the renormalized conduction-band energy spectrum at higher dop-ing n=4.5,12×1013cm-2, and find that the electron-phonon interaction effect on the band-structure renormalization becomes larger with increasing doping. This situation is in agreement with the ARPES data and the first-principles calculations. Our calculations reveal phonon-induced kinks near the Fermi energy at binding energies between175and220meV, in good agreement with experimental photoe-mission maps. Then we calculate the Fermi-level renormalizations, and find that the Fermi level∈F is shown to be lifted by5-20meV from the Fermi level∈F0without electron-phonon interaction in the range360-1200meV upon doping. Our results are smaller than that calculated in some paper. The effective electron-phonon cou-pling parameter is found to be λeffph=0.0084for∈F. The mass-renormalization pa-rameter λeff～10-13%within the doping range n=1.0×1013-12.0×1013cm-2. The λeff is smaller than calculated in the paper as mentioned above. We also carry out calculation of the spectral function at finite temperature (T=25K) and find that the shape and position of the kink at doping n=12.0x1013cm-2is in accord with the first-principles calculations.2. We have solved the strong-coupling self-consistent equations of a2D elec-tron-phonon interaction system numerically for different chemical potentials. We have also obtained self-energy, momentum distribution curves, electron distribution function at a finite temperature, and the relationship between chemical potential and the electron density. We find that the effect of electron-phonon interaction 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. The renormalization of the chemical potential is about10%at μ=0.30eV. And we find that the electron distribution functions with electron-phonon interaction at zero temperature are very similar to the electron distribution function at a finite temperature.