Time-resolved photoemission orbital tomography – mathematics and experiment

• Applicants: Professor Dr. David Russell Luke; Professor Dr. Stefan Mathias
• Subject Area: Experimental Condensed Matter Physics ; Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566257456

The ultimate access to all electronic, optical, and chemical properties of atoms, molecules and materials is represented by the full knowledge of the quantum-mechanical electron wave functions. In 2009, Puschnig et al. have shown in a seminal experiment that angle-resolved photoelectron spectroscopy (ARPES) measurements can be used to determine real-space orbital wave functions of adsorbed molecules on a surface, a technique which they termed Photoemission Orbital Tomography (POT). Since then, several breakthroughs in POT have been achieved, however the main challenges to achieving the full potential of this method, i.e. of time-resolved three-dimensional orbital imaging, lies in the development of suitable mathematical models, experimental techniques and algorithms. In this project we plan to study tomographic reconstruction on spherical shells in the context of ARPES and develop numerical algorithms and attendant convergence theory for phase retrieval in this nonlinear setting. The proposed research focuses in particular on time-resolved three-dimensional orbital tomography studies in hybrid organic-inorganic heterostructures, both in developing the technique and the mathematical description and tools. Moreover, we plan to extend the technique into the attosecond regime, where photoelectron density reconstruction methods become important for the interpretation of the data. We will also explore explicit wavefunction approximations of electronic orbitals combined with prior constraints. Such prior constraints allow us to incorporate the curvature of the measurement spheres leading to recovery algorithms in nonlinear metric spaces, the theory for which has been established in. Additionally, we will explore embedding vector scattering models accounting for field polarization into the above-mentioned settings.

• DFG Programme: Research Grants