Topological quantum phase transition in individual Fe Atoms on MoS$_2$/Au(111)

In a recent experiment [Trishin et al., Phys. Rev. Lett. 127, 236801 (2021)] a rich physics was observed for Fe atoms on MoS$_2$/Au(111), characterized by three different behaviors depending on the spectral density of the substrate $\rho_c$: one dominated by a single ion anisotropy, one by the Kondo effect, and an intermediate one. Based on symmetry and previous works, we show that the appropriate model to describe the system is the anisotropic two-channel spin-1 Kondo model (A2CS1KM), which has an underlying topological quantum phase transition (TQPT) between an ordinary Fermi liquid and a topological one with a non-trivial value of the Luttinger integral. Solving the model with the numerical renormalization group (NRG), we show that the different behaviors can be explained in a unified fashion as a function of $\rho_c$, and correspond to both Fermi liquids and an intermediate regime close to the TQPT in the topological phase. Further experiments should confirm this transition.