Embedded Green-function formulation of tunneling conductance: Bardeen versus Landauer approaches

Electron tunneling is described in a single particle picture as provided by the solutions of the Kohn-Sham equations in density functional theory. We reformulate the two most widely used approaches to single particle electron transport, the Landauer formula and the Bardeen approach, in terms of an embedding Green-function formulation. Both formulas are compared both for a simple analytic model as well as for a more realistic setup of a vacuum barrier between Cu(111) surfaces. We argue that Bardeen's approach provides a description of the noncoherent tunnel contribution due to localized surface or interface states relevant in realistic tunnel junctions.