Ab initio study of a mechanically gated molecule: From weak to strong correlation

The electronic spectrum of a chemically contacted molecule in the junction of a scanning tunneling microscope can be modified by tip retraction. We analyze this effect by a combination of density-functional, many-body perturbation, and numerical renormalization-group theories taking into account both the nonlocality and the dynamics of electronic correlation. Our findings, in particular the evolution from a broad quasiparticle resonance below to a narrow Kondo resonance at the Fermi energy, correspond to the experimental observations.

Figure 1

DFT-LDA structure of tip/PTCDA/Ag(111) junction. (a) and (b) Two representative configurations at tip-surface distances of $z=7$ and 10 Å, respectively. For better visibility only a section of the tip and the substrate are shown.

Figure 2

(a) HOMO and LUMO energies of gas-phase PTCDA and PTCDA/Ag(111) (peak of the PDOS; without STM tip). Experimental data are from Refs.27, 28 (gas phase), and 14 [on Ag(111)]. The two energy scales differ by $E_F=E_{\mathrm{vac}}-E_W$ [$E_W$ $=$ work function of Ag(111)]. (b) and (c) LUMO spectra for the tip/PTCDA/Ag(111) junction at tip heights of $z=8$ Å and $z=11$ Å. The experimental spectra are cuts through the $dI/dV$ map of panel d, at $z$ values of 7.5 Å and 9 Å. (d) LUMO peak positions and experimental $dI/dV$ color map, ranging from 0 $G_0$ (light blue) to 0.10 $G_0$ (yellow). Experiments were performed by approach-retraction cycles of the tip, with bias voltages increasing in steps of 1 mV. $dI/dV$ was detected with a lock-in amplifier, modulation amplitude 4 mV and modulation frequency 2.9 kHz. For bias voltages exceeding $\pm$100 meV, the tip-PTCDA contact becomes unstable. The experimental data point at ($z=5$ Å, $E=-0.45$ eV) is an estimate from Ref. 2 ($-$0.35 eV with the tip attached to the PTCDA monolayer) and Ref. 26 (the difference $-$0.1 eV between single-molecule and monolayer spectra).

Figure 3

Properties of the PTCDA LUMO at varying tip-surface distances $z$. (a) Mean-field QP correction (from LDA + $GdW$) of the LUMO for various occupancies, i.e., (from top to bottom) for the state being empty, being partially occupied (at $n_{\mathsf{LDA}+GdW}$), and being filled. (b) Intrastate interaction $U$ [from Eq. (4)]. (c) Occupancy of the LUMO from the various methods. Note that $n$ refers to one spin channel and the total number of electrons in the state is 2$n$. (d) Resulting Kondo temperature.