Inverse Isotope Effect on Kondo Temperature in Electron-Rattling System

In an electron system coupled with anharmonic phonons, i.e., {\it rattling}, inverse isotope effect on the Kondo temperature $T_{\rm K}$ is found to occur by the numerical evaluation of the Sommerfeld constant $\gamma$ of the Anderson-Holstein model. For the anharmonic potential of an oscillator with mass $M$ in which large $\gamma$ has been found to be almost independent of an applied magnetic field, $\gamma$ is significantly suppressed when $M$ is increased, i.e., $T_{\rm K}$ is enhanced due to the relation of $\gamma$$\sim$$T_{\rm K}^{-1}$ in the Kondo problem, leading to the inverse isotope effect on $T_{\rm K}$. Since this phenomenon does not occur for harmonic phonons, it can be a key experiment to prove the relevance of rattling to magnetically robust heavy electron state.