Role of excited states in the low-temperature dynamics of tunneling centers in metals: The orbital Kondo effect

We examine the interaction between a tunneling atom moving in a double potential well and the conduction electrons when the electron-assisted hopping to the excited states of the tunneling particle is taken into account. Using the renormalization-group transformation we show that virtual electron assisted hoppings to the excited states play a determining role in the low-temperature dynamics of the tunneling center, which scales to the two-channel Kondo problem at low temperature. The Kondo temperature ${\mathit{T}}_{\mathit{K}}$ separating the high temperature and the strongly correlated regime can be either increased or decreased due to the virtual hoppings to the excited states depending on the actual value of the bare couplings. However, carrying out a model calculation we find that for the physically relevant model parameters ${\mathit{T}}_{\mathit{K}}$ is always increased by one or two orders of magnitude even if the direct assisted tunneling between the potential minima is ignored. Thus this model can resolve the long-standing problem that the ${\mathit{T}}_{\mathit{K}}$ estimated earlier has always been somewhat small.