  The evolution of electron conductance in the presence of inelastic effects is
studied as an atomic gold contact is formed evolving from a low-conductance
regime (tunneling) to a high-conductance regime (contact). In order to
characterize each regime, we perform density functional theory (DFT)
calculations to study the geometric and electronic structures, together with
the strength of the atomic bonds and the associated vibrational frequencies.
The conductance is calculated by first evaluating the transmission of electrons
through the system, and secondly by calculating the conductance change due to
the excitation of vibrations. As found in previous studies [Paulsson et al.,
Phys. Rev. B. 72, 201101(R) (2005)] the change in conductance due to inelastic
effects permits to characterize the crossover from tunneling to contact. The
most notorious effect being the crossover from an increase in conductance in
the tunneling regime to a decrease in conductance in the contact regime when
the bias voltage matches a vibrational threshold. Our DFT-based calculations
actually show that the effect of vibrational modes in electron conductance is
rather complex, in particular when modes localized in the contact region are
permitted to extend into the electrodes. As an example, we find that certain
modes can give rise to decreases in conductance when in the tunneling regime,
opposite to the above mentioned result. Whereas details in the inelastic
spectrum depend on the size of the vibrational region, we show that the overall
change in conductance is quantitatively well approximated by the simplest
calculation where only the apex atoms are allowed to vibrate. Our study is
completed by the application of a simplified model where the relevant
parameters are obtained from the above DFT-based calculations.
