| Abstract [eng] |
Determination of Electron-electron Iinteraction in Graphene Using Scattering Matrix Approach Graphene is a carbon allotrope and a modern artificial material posessing unique properties. Its most interesting and promising properties are electronic. Vanishing bandgap in intrinsic graphene can be tunable in various ways, and high electron mobility makes it a possible candidate for future electronic devices. Currently, numerous graphene properties have been well explained using one-electron approximation, neglecting many-body physics. However, for certain effects Coulomb electron-electron interaction can be of greater importance. One way to probe it is by applying nonlinear spectroscopy techniques, such as 2D spectroscopy. Information retrieved from a 2D spectrum can show relaxation and screening effects. Therefore, the goals of this work are 1) to theoretically describe and calculate electron-electron Coulomb interaction using scattering matrix approach and 2) to simulate 2D spectrum of graphene for energies in vanishing bandgap region and evaluate its dependence on screening strength in graphene. In this work Coulomb interaction Hamiltonian has been derived in antisymmetric 2-electron wavefunctions set; Hamiltonian was grouped into blocks corresponding to different sublattice position and spin of electrons. The scattering matrix and the contribution of each block to 2D spectra have been calculated. Results show that in the linear dispersion region under consideration 2D spectra do not have expressed maxima or minima; among all blocks the Hamiltonian block of antisymmetric 2-electron wavefunctions and its 2D spectrum contribution are the most sensitive to electron-electron interaction screening length; and that on-diagonal values of the 2D spectrum corresponding to nonlinear absorption are of approximately linearly growth with relation to excitation energy. |
