We present a theory of temperature-dependent photoemission which accurately describes phonon effects in soft and hard x-ray angle-resolved photoemission. Our approach is based on a fully relativistic one-step theory of photoemission that quantitatively reproduces the effects of phonon-assisted transitions beyond the usual $\mathbf{k}$-conserving dipole selection rules which lead to the so-called XPS limit in the hard x-ray and/or high temperature regime. Vibrational atomic displacements have been included using the coherent potential approximation in analogy to the treatment of disordered alloys. The applicability of this alloy analogy model is demonstrated by direct comparison to experimental soft x-ray data from W(110) showing very satisfying agreement.

• Received 21 February 2013

DOI:https://doi.org/10.1103/PhysRevB.88.205409