Nonadiabatic interaction between electrons and Jahn-Teller distortions in a silicon vacancy

Recently, Goto et al. have discovered anomalous elastic softening due to vacancy in crystalline silicon at very low temperature. To investigate the quantum state of the silicon vacancy, we introduce a cluster model which includes the electron-lattice coupling between electrons and Jahn-Teller distortions together with the Coulomb interaction between electrons. By using the numerical diagonalization method, we take into account of both the nonadiabatic and the correlation effects. We find that the 3-fold orbital degeneracy in the ground state of a silicon vacancy is stable against the Jahn-Teller distortions because of the strong quantum fluctuation due to the nonadiabatic coupling between electrons and Jahn-Teller distortions. The obtained result is a striking contrast to the previous theoretical results within the adiabatic approximation and is consistent with the newly observed experiment