Vibration of the Dimer on Ge(001) Surface Excited Coherently by STM Current

The vibration of the dimer on Ge(001) surface with the higher vibrational number excited coherently by STM current is theoretically investigated. The coherent excitation rate of the dimer vibration is obtained by the Hamiltonian consisting of the terms of the electron system and the electron-vibration coupling terms. The transformation of the local structures reported in STM experiments is shown to be driven by the dimer vibration excited coherently by the STM current. The sample bias voltage of STM above which the transtormation to the p(2$\times$2) structure is able to be observed in the experiments, is semiquantitatively reproduced by the quasi-one-dimensional character of the $\pi^*$-band. We show that the excitation rate has the term not decaying on the distance from the STM tip for the one-dimensional band. The contrastive diffrence of the shapes of the transformed region depending on the sign of the bias voltage observed by the experiments is explained by the difference between the quasi-one-dimensional character of the $\pi^*$-band and the two-dimensional character of the $\pi$-band on Ge(001) surface.