Mechanical dissipation at a tip-induced Kondo onset

The onset or demise of Kondo effect in a magnetic impurity on a metal surface can be triggered, as often observed, by the simple mechanical nudging of a tip. This mechanically-driven quantum phase transition must reflect in a corresponding mechanical dissipation peak; yet, this kind of effect has not been focused upon so far. Aiming at the simplest theoretical modeling, we initially treat the impurity as a non-interacting resonant level turned cyclically on and off, and obtain a dissipation per cycle which is proportional to the hybridization $\Gamma$, with a characteristic temperature dependent resonant peak value. A better treatment is obtained next by solving an Anderson impurity model by numerical renormalization group. Here, many body effects yield a dissipation whose peak value is now proportional to $T_K |\log T|$ so long as $T\sim T_K$, followed for $T\sim \Gamma$ by a second high temperature regime where dissipation is proportional to $\Gamma|\log T|$. The detectability of Kondo mechanical dissipation in atomic force microscopy is discussed.