Theory of Bilayer Graphene Spectroscopy.

Mucha-Kruczynski, Marcin (2010) Theory of Bilayer Graphene Spectroscopy. PhD thesis, Lancaster University.

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Abstract

In this thesis, we model theoretically spectra measured for bilayer graphene obtained using the angle-resolved photoemission spectroscopy, magneto-optical absorption spectroscopy and electronic Raman spectroscopy The theories are based on the tight-binding description of the pi bands in the material. In particular, we concentrate on the comparison of the four-band model and its effective low-energy approximation neglecting the split high-energy bands, in the description of specific spectra. We demonstrate that both for monolayer and bilayer graphene, the observed anisotropy of angle-resolved photoelectron spectroscopy spectra reflects the electronic chirality in the system. However, for bilayer graphene, the influence of the nonchiral dimer states not captured within the effective approximation is significant and should not be neglected. We also show that the anisotropy of the constant-energy maps may be used to extract information about the magnitude and sign of interlayer coupling parameters and about symmetry breaking inflicted on a bilayer by the underlying substrate. We then determine selection rules and optical strengths of the inter-Landau-level excitations among any of the pi bands and including the physically most relevant symmetry-breaking parameters. We then present a self-consistent calculation of the interlayer asymmetry caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally. We also analyse the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers. Finally, we investigate the contribution of the low-energy electronic excitations toward the Raman spectrum of bilayer graphene for the incoming photon energy Ω " 1eV. Using the four-band model, we de rive an effective scattering amplitude that can be incorporated into the two-band approximation and show that this amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n- --->n+ inter-Landau-level transitions with crossed polarization of in/out photons. We estimate the quantum efficiency of a single n- ---> n+ transition in the magnetic field of 10 T as In- -> n+ ~ 10. 12.