Kondo Temperature for the Two-Channel Kondo Models of Tunneling Centers

The possibility for a two-channel Kondo ($2CK$) non Fermi liquid state to appear in a metal as a result of the interaction between electrons and movable structural defects is revisited. As usual, the defect is modeled by a heavy particle moving in an almost symmetric double-well potential (DWP). Taking into account only the two lowest states in DWP is known to lead to a Kondo-like Hamiltonian with rather low Kondo temperature, $T_K$. We prove that, in contrast to previous believes, the contribution of higher excited states in DWP does not enhance $T_K$. On the contrary, $T_K$ is reduced by three orders of magnitude as compared with the two-level model: the prefactor in $T_K$ is determined by the spacing between the second and the third levels in DWP rather than by the electron Fermi energy. Moreover, $T_K$, turns out to be parametrically smaller than the splitting between the two lowest levels. Therefore, there is no microscopic model of movable defects which may justify non-Fermi liquid $2CK$ phenomenology.