Theoretical study of the effects of electron-phonon and electron-photon interaction in optoelectronic properties of armchair graphene nano-flakes -a renormalization method

摘要

In this work, we study the effects of electron-phonon and electron-photon interaction on the electronic and optoelectmnic properties of nano systems consisting of graphene nano-flakes (small length armchair graphene nanoribbons) connected to two semi-infinite metal electrodes. Our calculations are based on the use of no-nequilibrium Green's function formalism. The non-interacting Hamiltonian is written within the nearest neighbor tight binding approximation. The full interacting Hamiltonian is then obtained by addition the electron-phonon and electron -photon interaction to the above non-interacting Hamiltonian. Using unitary transformations the interacting Hamiltonian is renormalized into a non-interacting tight-binding form with effective onsite energy and hopping parameter which contain the interacting effects. The Landuer-Buttiker formalism can now be used for the system with renormalized non-interacting Hamiltonian for calculating the electronic current. Within the above framework, we calculate the electron current, density of states (DOS) and photocurrent in the presence and absence of electron-phonon interaction in a nano-system consisting of graphene nano-flake with different width as central molecule. Our results show that electron-phonon interaction leads to decreasing the number of peaks in the DOS. Also the photocurrent has oscillatory behavior versus electron-photon coupling for different widths of the nano-flake. Finally, incident photon energy dependence of threshold electron-photon coupling (i.e photocurrent becomes larger than Ballistic case) and its increasing trend versus photon energy are studied.