Probing local moments in nanographenes with electron tunneling spectroscopy

The emergence of local moments in graphene zigzag edges, grain boundaries, vacancies and sp³ defects has been widely studied theoretically. However, conclusive experimental evidence is scarce. Recent progress in on-surface synthesis has made it possible to create nanographenes, such as triangulenes, with local moments in their ground states, and to probe them using scanning tunneling microscope (STM) spectroscopy. Here we review the application of the theory of sequential and cotunneling transport to relate the $\mathrm{dI}/\mathrm{dV}$ spectra with the spin properties of nanographenes probed by STM. This approach permits us to connect the $\mathrm{dI}/\mathrm{dV}$ with the many-body energies and wavefunctions of the graphene nanostructures. We apply this method describing the electronic states of the nanographenes by means of exact diagonalization of the Hubbard model within a restricted Active Space. This permits us to provide a proper quantum description of the emergence of local moments in graphene and its interplay with transport. We discuss the results of this theory in the case of diradical nanographenes, such as triangulene, rectangular ribbons and the Clar’s goblet, that have been recently studied experimentally by means of STM spectroscopy. This approach permits us to calculate both the $\mathrm{dI}/\mathrm{dV}$ spectra, that yields excitation energies, as well as the atomically resolved conductivity maps, that provide information on the wavefunctions of the collective spin modes.