Renormalization of spin excitations and Kondo effect in open-shell nanographenes

Abstract

We study spin excitations and the Kondo effect in open-shell nanographenes, motivated by recent scanning tunneling inelastic spectroscopy experiments. Specifically, we consider three systems: the triangulene, the extended triangulene with rocket shape, both with an S = 1 ground state, and a triangulene dimer with S = 0 on account of intermolecular exchange. We focus on the consequences of hybridization of the nanographene zero modes with a conducting substrate on the dI/dV line shapes associated with spin excitations. The partially filled nanographene zero modes coupled to the conduction electrons in the substrate constitute multiorbital Anderson impurity models that we solve in the one-crossing approximation, which treats the coupling to the substrate to infinite order. We find that the coupling to the substrate leads to (i) renormalization of the spin flip excitation energies of the bare molecule, (ii) broadening of the spectral features, and (iii) the emergence of zero bias Kondo peaks for the S = 1 ground states. The calculated substrate induced shift of the spin excitation energies is found to be significantly larger than their broadening, which implies that this effect has to be considered when comparing experimental results and theory.

Observation of fractional edge excitations in nanographene spin chains

“…6). Deviations between theory and experiments can be partially accounted for by the renormalization of excitation energies due to interactions with the metal surface 37,38 . Second, with the exception of the N = 3 TSC, the energy of the lowest energy spin excitation progressively decreases with increasing N, as predicted by the BLBQ model (Fig.…”

Aza-Triangulene: On-Surface Synthesis and Electronic and Magnetic Properties

“…As a result, the twofold symmetric vertex of the molecule remains with a lower electronic density but higher spin density (Figure 5d). 57 Positively and negatively charged aza-triangulene molecules (7 + and 7 − ) hold an even number of p z electrons, allowing for an equal population of the e″ frontier orbital pair. In 7 + , the e″ space is partially occupied and vibronic couplings inducing D 3h → C 2v Jahn−Teller distortion, as in neutral 7, compete with Hund's-rule coupling emerging from Coulomb repulsion and exchange interaction of the two electrons in the two e″ orbitals.…”

“…Frontier orbitals of the C 2 v structure (a 2 and b 2 ; Figure f) present spatial distributions similar to the e″ pair in the D 3 h arrangement, with two electrons filling the b 2 orbital and one in the a 2 orbital localized on the molecular vertex crossed by the C 2 axis. As a result, the twofold symmetric vertex of the molecule remains with a lower electronic density but higher spin density (Figure d) …”

Frustrated magnetic interactions in a cyclacene crystal

“…In principle, the fate of these magnetic configurations might change due to interactions with the substrate. On the theory front, a previous work by two of us [63] shows that coupling to a conducting surface indeed renormalizes the 014406-6 spin excitation energies, but does not eliminate the openshell nature of the nanographenes. In addition, there is now a growing body of experimental work reporting magnetism on nanographenes deposited on gold [8][9][10][11][12][13]64].…”