  The ab initio calculation with the density functional theory and plane-wave
bases is carried out for stepped Si(111)-2x1 surfaces that were predicted in a
cleavage simulation by the large-scale (order-N) electronic structure theory
(T. Hoshi, Y. Iguchi and T. Fujiwara, Phys. Rev. B72 (2005) 075323). The
present ab initio calculation confirms the predicted stepped structure and its
bias-dependent STM image. Moreover, two (meta)stable step-edge structures are
found and compared. The investigation is carried out also for Ge(111)-2x1
surfaces, so as to construct a common understanding among elements. The present
study demonstrates the general importance of the hierarchical research between
large-scale and ab initio electronic structure theories.
