Electrons in crystalline solids can only occupy quantum states of certain energy and momenta, others being unoccupied thus forming a continuum of states known as the band structure of the solid. Most of the physical properties of solids are determined by its electronic band structure near the Fermi energy and angle-resolved photoemission spectroscopy is one of the most powerful and interesting experimental technique to map the whole E-k diagram with a very high energy and momentum resolution. In this talk, I will discuss the mightiness of this indispensable technique with a few simple experimental results of novel 2D materials as examples.

Starting from textbook results on partial waves, I will introduce Green's function (propagators), transition and scattering path operators. Then, I will apply this formalism to core-level spectroscopies, such as photoelectron diffraction, and show how to calculate the key ingredients in order to model the cross-section. Applications to photoelectron diffraction spectra will be made in the hands-on course.

ime-resolved reflection spectroscopy provides a direct window into the ultrafast response of magnetic materials when perturbed by femtosecond laser pulses. I will begin with a brief introduction to the basics of pump–probe spectroscopy—how transient changes in optical constants encode the underlying electronic, lattice, and spin dynamics. The focus of the talk will be our recent work on the layered magnet CrSiTe₃[1], where we use optically generated picosecond strain pulses to investigate the magnetic dimensional crossover from 2D to 3D behavior. As the system approaches this crossover, the reflectivity transients exhibit distinct strain-coupled signatures that sensitively track the evolution of critical spin fluctuations. By analyzing these strain-modulated dynamics, we uncover the characteristic timescales and coupling strengths that reveal how the lattice influences the magnetic free energy landscape during the 2D–3D transition. Overall, the talk will show how ultrafast reflection spectroscopy combined with dynamic strain engineering provides a powerful method to probe and control emergent magnetic behavior in van der Waals materials such as CrSiTe₃.

1. "Probing of magnetic dimensional crossover in CrSiTe3 through picosecond strain pulses", Anjan Kumar N M, Soumya Mukherjee, Abhirup Mukherjee, Ajinkya Punjal, Shubham Purwar, Thirupathaiah Setti, Shriganesh Prabhu S, Siddhartha Lal, N. Kamaraju, Phys. Rev. B 111, L140414 (2025).

Quantum materials exhibit a complex interplay between electronic correlations, topology, and magnetism, placing them at the forefront of condensed matter physics and quantum technology. Understanding these systems requires disentangling spin-orbit coupling, electron-electron interactions, and magnetic fluctuations under realistic conditions, including finite temperatures and structural disorder. Spin- and time-resolved angle-resolved photoemission spectroscopy (STARPES) is a crucial technique for probing electronic and spin structures in magnetic and topological materials. However, quantitative interpretation of spin-ARPES data necessitates advanced theoretical models that accurately capture electronic states, spin textures, and dynamic responses to external fields. I will present a theoretical framework based on the fully relativistic multiple-scattering Green function KKR method [1], effectively modeling spin-dependent photoemission. This approach includes correlation effects via dynamical mean-field theory (DMFT) [2] and describes spin fluctuations using the alloy analogy model [3]. I will also discuss advances in calculating light-induced electronic excitations [4], highlighting their relevance to spin-ARPES studies of topological and magnetic quantum materials. A novel application is the one-step model of photoemission in studying altermagnets and kagome magnetic materials. Altermagnets, exhibiting unconventional time-reversal symmetry breaking without net magnetization, are explored in RuO2 and MnTe [5,6]. Spin-ARPES combined with the one-step model provides insights into lifted Kramers spin degeneracy, revealing their potential for spintronics. In kagome magnetic materials, persistent flat band splitting and selective band renormalization are observed in FeSn thin films [7], highlighting unique correlation effects and topological phenomena. These developments offer a comprehensive framework for exploring magnetic phenomena and spin dynamics in complex quantum materials. References:

[1] H. Ebert et al., Rep. Prog. Phys. 74, 096501 (2011). DOI: 10.1088/0034-4885/74/9/096501

[2] J. Minár, J. Phys.: Condens. Matter 23, 253201 (2011). DOI: 10.1088/0953-8984/23/25/253201

[3] J. Minár et al., Phys. Rev. B 102, 035107 (2020). DOI: 10.1103/PhysRevB.102.035107

[4] J. Braun et al., Physics Reports 749, 1 (2018). DOI: 10.1016/j.physrep.2018.02.007

[5] J. Krempaský et al., Nature 626, 517 (2024). DOI: 10.1038/s41586-023-06907-7

[6] O. Fedchenko et al., Sci. Adv. 10, eadj4883 (2024). DOI: 10.1126/sciadv.adj4883

[7] Z. Ren et al., Nature Communications 15, 9376 (2024). DOI: 0.1038/s41467-024-53722-3

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) has emerged as a powerful technique for probing and manipulating non-equilibrium quantum phenomena in solid quantum materials. In this talk, I will introduce the fundamental principles of TR-ARPES and provide an overview of the key components that define state-of-the-art TR-ARPES experimental setups.I will then highlight recent advances and results enabled by these capabilities, such as the direct visualization of the dark moiré interlayer excitons [1,2] and the observation of light-induced Floquet states in graphene [3],demonstrating how TR-ARPES reveals non-equilibrium quasiparticles formation and transient band renormalization under optical driving. Finally, I will briefly discuss severalemerging developments, including the multi-lens mode and spin-filter in time-resolved momentum microscopy [4]. [1]D. Schmitt et al., Nature608, 499 (2022). [2]D. Schmitt et al., Nat. Photon.19, 187-194 (2025). [3]M. Merboldt et al., Nat. Phys.21, 1093-1099 (2025). [4]O. Tkach and G. Schönhense, Ultramicroscopy276, 114167 (2024).