Unified Description of Inelastic Propensity Rules for Electron Transport through Nanoscale Junctions

Abstract

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmeties in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states -namely those belonging to the most transmitting eigenchannels -need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.Electronic transport through atomic-size junctions is of immense scientific and technological interest. The importance of inelastic effects in electronic currents have been revealed in several ground-breaking experiments leading to the detection and identification of single molecules [1], chemical reactions [2,3], the detection of vibrations in atomic wires [4], the detection of inelastic effects by fluorescence [5], the modification of electron transport in nanotubes [6], the molecular motion induced by electronic currents [7], and the hydrogen detection in atomic wires [8], just to cite a few examples. Of particular importance due to its spreading use is the case of vibrational spectroscopy where the conductance changes due to phonon emission is measured [9,10,11]. This is often referred to as point contact spectroscopy or inelastic electron tunneling spectroscopy (IETS) [1], However, experiments alone are not able to give direct insight into the fundamental question on how the detailed atomic structure correlate with the electrical transport properties. There is experimental evidence of approximate selection rules (propensity rules [12]) such that only a small number out of the many possible vibrational modes give an inelastic signal. These propensity rules yield clues to the geometric and electronic structure of the junctions. It is therefore of fundamental interest to compare the experimental results with first-principles calculations.Existing calculations of inelastic effects in electron transport have been developed either for particular cases [12,13,14] or for simplified (one-level) models [15,16]. First-principles methods capable of treating both weak and strong coupling to the electrodes has also been developed [17,18,19]. However, the results of such detailed calculations involve many electronic states and vibrational modes. An advanced analysis is therefore needed in order to provide insight into the propensity rules.In this paper we propose a method for analysis of the inelastic transport based on just a few selected electronic scattering states, namely those belonging to the most transmitting eigenchannels at the Fermi energy (ε f ) [20]. These scattering states typically have the largest amplitude inside the junction and thus account for the majority of the electron-phonon (e-ph) scattering. To illustrate our method of analysis and to develop an understanding of the propensity rules we consid...

Role of molecular electronic structure in inelastic electron tunneling spectroscopy:O2on Ag(110)

“…However, questioning the position of the Fermi level and, thus, the molecular charge state in this system is at variance with the excellent characterization of the two experimental chemisorption states given by DFT. 8 Moreover, the Fermi-level fitting, 20,22 thought to force the g resonance, cannot reproduce the rich IETS structure of the experimental data showing increases and decreases according to the vibrational mode and the tip localization.…”

“…The simulations give conductance increases because in the DFT electronic structure the g orbitals are not on resonance with the Fermi level. 20,22 This discrepancy led to speculate that the theoretical Fermi level was wrongly positioned. However, questioning the position of the Fermi level and, thus, the molecular charge state in this system is at variance with the excellent characterization of the two experimental chemisorption states given by DFT.…”

“…It is generally admitted that in tunneling, the excitation of a vibration mode leads to opening an inelastic channel for conduction, hence increasing the conductance. [18][19][20][21] However, early model calculations predicted that when a molecular resonance overlaps the Fermi level of the substrate, IETS could also give rise to decreases in conductance. 18 Up to now, the O 2 ͓001͔ is the only example, where such decreases in conductance have been observed experimentally.…”

Lowest order in inelastic tunneling approximation: Efficient scheme for simulation of inelastic electron tunneling data

“…31 It also enables a particularly simple derivation of the IETS rules which govern the inelastic activity of a given mode. 34 The paper is organized as follows. In Sec.…”

Surveying Molecular Vibrations during the Formation of Metal−Molecule Nanocontacts

“…17 To obtain a physical understanding of the experimentally observed frequency shifts, we have modeled the vibration modes and the inelastic transport using density functional theory (DFT) combined with nonequilibrium Green's function methods. 22,23 In our calculations the STM tip is modeled by a Cu adatom adsorbed on a Cu(111) surface at a face-centered cubic (fcc) hollow site. To simulate the inelastic electron tunneling spectra, we have assumed the adsorption site of CO on a top-site of Cu(111), as experimentally observed (scheme in Figure 2b).…”