Elastic and inelastic scattering effects in conductance measurements at the nanoscale : A theoretical treatise

Abstract: Elastic and inelastic interactions are studied in tunnel junctions of a superconducting nanoelectromechanical setup and in response to resent experimental superconducting scanning tunneling microscope findings on a paramagnetic molecule. In addition, the electron density of molecular graphene is modeled by a scattering theory approach in very good agreement with experiment. All studies where conducted through the use of model Hamiltonians and a Green function formalism. The nanoelectromechanical system comprise two fixed superconducting leads in-between which a cantilever suspended superconducting island oscillates in an asymmetric fashion with respect to both fixed leads. The Josephson current is found to modulate the island motion which in turn affects the current, such that parameter regions of periodic, quasi periodic and chaotic behavior arise. Our modeled STM setup reproduces the experimentally obtained spin excitations of the paramagnetic molecule and we show a probable cause for the increased uniaxial anisotropy observed when closing the gap distance of tip and substrate. A wider parameter space is also investigated including effects of external magnetic fields, temperature and transverse anisotropy. Molecular graphene turns out to be well described by our adopted scattering theory, producing results that are in good agreement with experiment. Several point like scattering centers are therefore well suited to describe a continuously decaying potential and effects of impurities are easily calculated.