Absolute Band Mapping by Combined Angle-Dependent Very-Low-Energy Electron Diffraction and Photoemission: Application to Cu

Abstract

We present an experimental method to determine the electronic $E\left(\mathbf{k}\right)$ band structure in crystalline solids absolutely, i.e., with complete control of the three-dimensional wave vector $\mathbf{k}$. Angle-dependent very-low-energy electron diffraction is first applied to determine the unoccupied states whose $\mathbf{k}$ is located on a high-symmetry line parallel to the surface. Photoemission via these states, employing the constant-final-state mode, is then utilized to map the valence bands along this line. We demonstrate the method by application to Cu, and find significant deviation from free-electron-like behavior in the unoccupied states, and from density-functional theory in the occupied states.