**Time- and Angle-Resolved Photoemission Spectroscopy of Quantum Materials - Our Approach **

Angle-Resolved Photoemission Spectroscopy (ARPES) is the experimental technique providing the most direct access to a crystal’s electronic structure. It relies on detecting the energy and the momentum of electrons that have been emitted from the surface of a crystalline solid through the photoelectric effect. ARPES allows for the complete reconstruction of solids' occupied electronic band structure.

Knowledge about the electronic band structure, i.e., the momentum-dependent energy eigenvalues, and the associated Bloch wave function is essential for understanding crystalline solids' transport, optical, and magnetic properties. With the discovery of topological materials, it became clear that accessing knowledge beyond the band structure is fundamental to understanding the unique properties of this important class of quantum materials. The topologically nontrivial nature of materials emerges from the winding of the phase of their Bloch wave functions in momentum space, associated with Berry curvature and topological invariants. Reconstructing the band structure *and* the associated Bloch wave function is thus of capital importance to fully characterize the electronic structure of (topological) materials. We are thus developing new measurement protocols in ARPES based on the modulation of the photoemission transition dipole matrix element. These schemes are based on measuring the modification of the energy- and momentum-resolved photoemission yield upon tailoring light-matter interaction symmetries, e.g. using original XUV polarization state shaping and crystal rotation, allowing for generating new differential observables.

These novel measurement methodologies in ARPES, in combination with advanced theories, add new dimensions to obtaining insights into the orbital pseudospin, Berry curvature, and Bloch wave functions of many relevant crystalline solids. We are particularly interested in the investigation of 2D quantum materials.

Because quantum materials exhibit extreme responses to external stimuli, using femtosecond light pulses to induce ultrafast modifications of population, symmetry, topology, and many-body interactions upon photoexcitation can be used to transiently tailor the properties of quantum materials. We are thus using time-resolved ARPES as an ultrafast and quantum-state-resolved probe of the out-of-equilibrium electronic structure of photoexcited quantum materials. In addition, we envision extending the above-described novel measurement methodologies to the time-resolved investigation of out-of-equilibrium dynamics of photoexcited solids. This will be enabled thanks to the development of a high-repetition-rate, polarization-tunable, monochromatic (21.6eV) XUV beamline, which was specifically designed for this purpose.