Photoemission orbital tomography provides a unique access to the real-space molecular orbitals of well-ordered organic semiconductor layers. Specifically, the application of phase retrieval algorithms to photon-energy- and angle-resolved photoemission patterns enables the reconstruction of full 3D molecular orbitals independent of density functional theory calculations. However, until now this procedure has remained challenging due to the need for densely-sampled, well-calibrated 3D photoemission data. Here, we present an iterative projection algorithm that completely eliminates this challenge: For the benchmark case of the Pentacene frontier orbitals, we demonstrate reconstruction of the full orbital based on a data set containing only seven photoemission momentum maps. Based upon application to simulated data, we discuss the algorithm performance, sampling requirements with respect to the photon energy, optimal measurement strategies and the accuracy of orbital images that can be achieved.

Photoemission Orbital Tomography (POT) is a powerful tool for probing the full electronic structure of oriented molecular thin films which allows a direct comparison of angle-resolved photoemission spectroscopy (ARPES) data with density functional theory calculations. Moreover, the application of numerical phase retrieval algorithms in the POT framework has enabled a complete recovery of the initial molecular orbital independent of theoretical calculations [1, 2]. In combination with ultrafast pump-probe spectroscopy this approach promises to image excited state wavefunctions with Angstrom-level spatial and femtosecond temporal resolution.

However, most POT experiments to date have been restricted to a single probe photon energy, providing only a two-dimensional view of the initial wavefunction. This has limited the access to the full three-dimensional wavefunction to specialized, synchrotron-based facilities, where the implementation of femtosecond time-resolved experiments is challenging. At the same time, a time-resolved access to the third dimension is highly desirable, as it would enable the study of light-induced charge-transfer processes at hybrid molecular interfaces.

We overcome this limitation by implementing an EUV monochromator into the existing high harmonic generation beamline of our femtosecond photoemission setup with the ultimate goal of performing time-resolved three-dimensional orbital tomography. In this talk, I will report on our newly built-up setup and present our first energy-dependent photoemission data of molecules.

[1] P. Puschnig, S. Berkebile, A.J. Fleming, G. Koller, K. Emtsev, T. Seyller, J.D. Riley, C. Ambrosch-Draxl, F.P. Netzer, M.G. Ramsey. Reconstruction of Molecular Orbital Densities from Photoemission Data, Science 326: 702-706, 2009.

[2] G.S.M. Jansen, M. Keunecke, M. Düvel, C. Möller, D. Schmitt, W. Bennecke, F.J.S. Kappert, D. Steil, D.R. Luke, S. Steil, S. Mathia. Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval, New J. Phys. 22, 2020.

X-ray photoelectron diffraction (XPD) is a powerful technique that yields detailed structural information of solids and thin films that complements electronic structure measurements. Among the strongholds of XPD we can identify dopant sites, track structural phase transitions, and perform holographic reconstruction. High-resolution imaging of momentum-distributions (momentum microscopy) presents a new approach to core-level photoemission. It yields full-field XPD patterns with unprecedented acquisition speed and richness in details. Beyond the pure intensity-related diffraction information, XPD patterns exhibit pronounced circular dichroism in the angular distribution (CDAD) with asymmetries up to 80%. Experimental results for a number of examples prove that core-level CDAD is a general phenomenon that is independent of atomic number. Calculations using both the Bloch-wave approach and one-step photoemission reveal the origin of the fine structure that represents the signature of Kikuchi diffraction. Comparison to theory allow to disentangle the roles of photoexcitation and diffraction.

[1] O. Fedchenko, A. Winkelmann, K. Medjanik, S. Babenkov, D. Vasilyev, S. Chernov, C. Schlueter, A. Gloskovskii, Yu. Matveyev, W. Drube, B. Schönhense, H.J. Elmers, G. Schönhense. High-resolution hard-x-ray photoelectron diffraction in a momentum microscope – The model case of graphite, New. J. Phys. 21, 2019.

[2] K. Medjanik, O. Fedchenko, O. Yastrubchak, J. Sadowski, M. Sawicki, L. Gluba, D. Vasilyev, S. Babenkov, S. Chernov, A. Winkelmann, H.J. Elmers, G. Schönhense. Site-specific atomic order and band structure tailoring in the diluted magnetic semiconductor (In, Ga, Mn) As, Phys. Rev. B 103, 2021.

This contribution will concentrate on three recent applications of photoemission orbital tomography (POT). First, results of an on-surface synthesized molecular layer will be presented, show-casing how the imaging of molecular orbitals using POT sheds light on surface chemical reactions. Second, it will be demonstrated how POT can be generalized to extended two-dimensional systems. On the example of a strongly-hybridising molecular overlayer on a Cu(110) surface, deep insights into the complicated interplay of bulk states, surface states, and molecular orbitals can be gained from the orbital imaging. Finally, experimental and theoretical results for monolayer graphene will be presented. Here, the photon energy dependence of photoemission intensities indicate limitations of the plane-wave final state approximation which is at the heart of POT. Validated by real-time time-dependent density functional calculations, we develop a simple and intuitive model which accounts for final state scattering, which should allow for the inversion of experimental data to real-space orbital images, thereby going beyond the plane-wave paradigm of POT.