Electronic States Caused by the Truncation of Crystal Periodicity

Abstract

What will happen when the 3D periodic crystal (bulk) is truncated? The surface may form the unique atomic and electronic structure quite different from its bulk. However, without such significant reconstruction, the truncation of the periodicity itself can play an important role for the two-dimensional electronic structure in the surface and subsurface region. To elucidate such sub-surface electronic structure, the origin of the two-dimensional surface states localized in subsurface regions of the Ge (111) substrate has been studied by angle-resolved photoelectron spectroscopy (ARPES) and density-functional-theory calculations. From the Ge (111) surfaces covered with various elements, we found the common 2D electronic states closely related to the bulk Ge bands nearby; the heavy-hole, light-hole, and spin-orbit split-off bands. These subsurface states originate from the bulk bands that are perturbed due to the truncation of the three-dimensional periodicity at the surface, which could be regarded as precursor electronic states to topological surface states that is, in most cases, also derived from the bulk bands.