Effect Of Hydrogen Dimer Adsorption And Electron Doping On The Electronic Structures Of Graphene

Graphene is a two-dimensional material that possess unique electronic structure. The two energy bands of graphene touch each other at six corners of Brillouin zone which are so-called Dirac points. So graphene is a zero-gap semiconductor. For the low energy ex-citation, the charge carriers in graphene are massless Dirac fermions which are governed by Dirac equation, and possess linear bands that cross at the Dirac points.Hydrogenation is an effective approach to open a band gap in graphene. Hydrogen atom adsorbed on the top of a site of graphene forms sp3 covalent bond with the host carbon atom. Hydrogen monomer adsorption on the graphene have been studied theoret-ically. Besides, three types of hydrogen dimer, ortho, meta and para dimers have been revealed in experiments and first-principle calculations. In this thesis, the three types of hydrogen dimer adsorption on graphene are investigated. Using the Green's function and T-matrix approach, we present analytic expression of the local density of states (LDOS)of graphene with single hydrogen dimer adsorption. We also calculate the quasiparticle spectral function of graphene with a finite concentration of randomly distributed hydrogen dimers.A kink structure in the quasiparticle spectrum of electrons in graphene is observed at 200 meV below the Fermi level in angle-resolved photoemission spectroscopy (ARPES)experiments. A theory of analytical calculation of electron-phonon (e-ph) interaction effects was developed by Tse and Das Sarma [Phys. Rev. Lett. 99, 236802 (2007)]. But their results were not consistent with the ARPES data and the first-principle calculations.In this thesis, we revisit this approach analytically.Furthermore, with the full band structure of graphene instead of linear energy spec-trum, we formulate the e-ph coupling due to the lattice vibration modulation of the near-est hopping energy in the tight-binding model of graphene. We numerically calculate the electron self-energy and the effect of e-ph coupling to the spectral function of quasipar-ticle in electron-doped graphene. All our results are compared with previous theoretical calculations.The main work in this thesis are listed as follows:1. We study the effect of hydrogen dimer adsorption on the electronic structures of graphene. Using the Green's function and the T-matrix approach, we calculate the LDOS of graphene with single hydrogen dimer, as well as the quasiparticle spectral function of graphene with a finite concentration of randomly distributed hydrogen dimers. Our results show that the meta dimer adsorption leads to a resonant peak in the LDOS just below the Dirac point, and induces a quasi band gap at the Dirac point within which localized states appear. These properties are similar to that of hydrogen monomer adsorption. On the contrary, both the ortho and para dimer adsorption give rise to the double-peak structure in the LDOS in the vicinity of the Dirac point, and are not able to open a band gap at the Dirac point in the spectral function of graphene. Instead, they induce the spectrum rearrangement at some momenta deviated from the Dirac points.2. We revisit e-ph interaction approach proposed in Tse and Das Sarma's paper, and analytically evaluate the electron self-energy in graphene. The imaginary part of self-energy we obtain is exactly as the same as that in Tse and Das Sarma's paper. However, the real part of self-energy have an extra item which does not appear in the results in Tse and Das Sarma's paper. We calculate the self-energy, the energy distribution curves, the quasiparticle spectral function and the effective mass-renormalization parameter for three different electron doping levers n =1.0,4.5,12.0×1013 cm-2. Our calculations reveal a kink structure below the Fermi level about 196 meV. For the doping level n = 1.0, 4.5, 12.0×1013 cm-2,the range of kink is about 10, 25, 45 meV, respectively. The range and sharpness of the kink are in good agreement with ARPES data and first-principle calculations.The effective mass-renormalization parameter ?eff is 10 ?13% within the doping range n = 1.0 ?12.0×1013 cm-2. This result is smaller than that in Tse and Das Sarma's paper.3. We formulate the e-ph coupling due to the lattice vibration modulation of nearest hopping energy in the tight-binding model in graphene. We numerically calculate the electron self-energy and the effect of e-ph coupling on the spectral function of quasiparticle in electron-doped graphene. Our results show the effect of e-ph coupling on the band structure renormalization is very slight at low doping level n=1.0×1013 cm-2, and the kink is hardly recognizable. At doping levels n=4.5, 12.0×1013 cm-2, a kink structure emerges at phonon energy h?0=196 meV below Fermi level. But the sharpness and strength of the kink are much smaller than previous calculations. The mass-renormalization parameter ?eff near the Fermi level is about 7?9% within the doping range n = 1.0?12.0 × 1013 cm-2. This value is smaller than that obtained in experiments and theoretical calculations. Our results suggest that the e-ph coupling due to the modulation nearest hopping energy is too weak to explain the kink structure observed in ARPES data and first-principle calculations.