Kondo conductance across the smallest spin 1/2 radical molecule

Abstract

Molecular contacts are generally poorly conducting because their energy levels tend to lie far from the Fermi energy of the metal contact, necessitating undesirably large gate and bias voltages in molecular electronics applications. Molecular radicals are an exception because their partly filled orbitals undergo Kondo screening, opening the way to electron passage even at zero bias. Whereas that phenomenon has been experimentally demonstrated for several complex organic radicals, quantitative theoretical predictions have not been attempted so far. It is therefore an open question whether and to what extent an ab initio-based theory is able to make accurate predictions for Kondo temperatures and conductance lineshapes. Choosing nitric oxide (NO) as a simple and exemplary spin 1/2 molecular radical, we present calculations based on a combination of density functional theory and numerical renormalization group (DFT+NRG), predicting a zero bias spectral anomaly with a Kondo temperature of 15 K for NO/Au(111). A scanning tunneling spectroscopy study is subsequently carried out to verify the prediction, and a striking zero bias Kondo anomaly is confirmed, still quite visible at liquid nitrogen temperatures. Comparison shows that the experimental Kondo temperature of about 43 K is larger than the theoretical one, whereas the inverted Fano lineshape implies a strong source of interference not included in the model. These discrepancies are not a surprise, providing in fact an instructive measure of the approximations used in the modeling, which supports and qualifies the viability of the density functional theory and numerical renormalization group approach to the prediction of conductance anomalies in larger molecular radicals.

Keywords: Anderson impurity model; ballistic conductance; nanocontacts; phase shift.

Fig. 1.

Model STM geometry for NO/Au(111). The scattering region shown contains one NO molecule and 28 Au atoms; it satisfies periodic boundary conditions in the transverse direction and is bounded by two planes in the c direction, where the potential is smoothly matched to the potential of bulk gold. NO is shown in the optimal on-top adsorption geometry, where the molecule is bent by about 60°. Figure produced using VESTA (46).

Fig. 2.

Projected density of states for NO/Au(111). Spin-up states are plotted as positive values and spin-down states as negative. The densities of states of the NO molecular orbitals (Insets) are estimated from weighted sums of the projections on N and O p orbitals. The Fermi energy is indicated by a vertical line. The states of NO and the states of the top-site Au atom, Au_top, are shifted and scaled for visibility.

Fig. 3.

STM/STS images and spectra, all obtained with clean Au tips except for B and C. (A) Isolated NO molecules (arrows) and small NO clusters on Au(111) at 5 K. (B and C) Two small NO clusters formed from a few molecules (in the center) and substrate Au atoms (at the edges) imaged with a molecule on the STM tip. The Au lattice is marked by blue dots. Most of the molecules are on top. (Scale bar, 0.5 nm.) (D) Filled-state STM image of an ordered single NO layer obtained after annealing at 70 K. The layer is made up of rows of units with a dumbbell shape that is consistent with the shape of the filled orbital. The arrows point to two of these units. (E) NRG spectral functions for the orbitals of NO at the on-top adsorption site calculated at 5 K with ab initio parameters from Table S2. Insets: spectral function (Left), Fano lineshapes (Upper Right), and interfering tunneling paths t₁ and t₂ (Lower Right). (F) Tunneling spectra of isolated molecules and small clusters at 5 K and clusters at 40 K and 68 K showing the Kondo dip. The spectra are shifted vertically for clarity. The solid lines are fits with the Frota function (31).

Fig. 4.

Temperature dependence of the HWHM of the Kondo resonance from experiment (red) and NRG calculations (black) based on the ab initio parameters for the on-top adsorption geometry (Table S2). Experimental error bars indicate the SD calculated from a collection of spectra on different NO molecules. Spectra were measured on at least 10 different molecules at each temperature. The error bars on the theoretical curve represent the uncertainty corresponding to a ±20% uncertainty in the hybridization linewidth; uncertainty from other parameters is not depicted. Model parameter SDs are reported in Table S2.