Linear and nonlinear optical properties of graphene nanodisk out of equilibrium

We explore linear and nonlinear optical polarizability of graphene nanodisk in nonequilibrium steady-state. By using nonequilibrium Greenʹs function formalism, we extend sum-over-state method of calculation of optical polarizabilities to nonequilibrium state for obtaining linear and nonlinear optical polarizability of current carrying clusters or molecules with interacting electrons. We apply this method for graphene nanodisks and use Hartree–Fock approximation to take into account the electron–electron interaction and utilize extended Su–Schrieffer–Heeger model to include the effect of lattice distortion and calculate first and third order polarizability of graphene nanodisks in equilibrium and nonequilibrium state. Our consideration shows that graphene nanodisks, in equilibrium state, have significant linear and nonlinear optical properties due to the planarity shape of nanodisks and existence of delocalized π-electrons. Also we find that optical polarizabilities of graphene nanodisks, like electrical current and their dimerization, vary step-like versus bias voltage and can be tuned by allowing the current to pass through them. It is found that these variations for large-size nanodisks are more evident and take place in lower bias voltage, specially their third harmonic generation which increases considerably, so the current carrying large-size graphene nanodisks can be prominent for nonlinear application in photonic devices.