Temperature-induced distortions of electronic states observed via forbidden Bragg reflections in germanium

According to the adiabatic approximation, the electronic states of atoms in solids are bound up with thermal atomic motion. As a result, thermal-motion-induced (TMI) anisotropy of x-ray susceptibility can appear for atoms occupying positions with high symmetry. We report evidence for this effect found in the very strong temperature dependence of the 006 forbidden Bragg reflections from a germanium single crystal. The intensity of these reflections increases or decreases drastically as the temperature rises from 30 K to 300 K, in contrast with nonforbidden reflections. It is found that the TMI anisotropy of the structure amplitude scales with the temperature as the mean square of the atomic displacements. This observation is very important for understanding the intricate interplay between phonon and electronic properties of solids.