The interplay of the spin and the orbital angular momenta of electrons in semiconductors governs the observed Zeeman splitting, often described by the effective g-factors. In the realm of 2D materials, transition metal dichalcogenides (TMDCs) are ideal candidates to explore the manifestation of coupled spin and orbital degrees of freedom under external and synthetic magnetic fields. In this talk, I will discuss two types of valley splitting signatures in TMDC-based van der Waals heterostructures: (i) effective g-factors in the presence of an external magnetic field, and (ii) nonzero valley Zeeman due to proximity exchange effects. I will cover the basic physics behind the effective g-factors, emphasizing the recent rst-principles developments that nicely reproduce the experiments in pristine[1] and strained[2] monolayer TMDCs. Employing this formalism to TMDC-based van der Waals heterostructures, particularly MoSe2/WSe2[1,3] systems, I will show that the spinvalley physics and g-factors encode valuable information about the stacking conguration and interlayer coupling. For the proximity exchange effects, I will focus on (Mo,W)Se2 on the ultrathin vdW ferromagnet CrI3[4], and (Mo,W)S2/hBN on conventional Co and Ni ferromagnets[5]. Systematically combining ab initio investigations, phenomenological modeling of the band structure and subsequent excitonic calculations, we reveal important microscopic features and signatures of the proximity exchange: despite being short ranged, these effects can be strongly tailored by external electric fields and the twist angle between the layers.

[1] Wozniak, Faria Junior et al., PRB (Editors' Suggestion) 101, 235408 (2020).
[2] Faria Junior et al., New J. Phys. 24, 083004 (2022). Blundo, Faria Junior et al., Phys.
Rev. Lett. 129, 067402 (2022). Covre, Faria Junior et al., Nanoscale 14, 5758 (2022).
[3] Faria Junior, Fabian, Nanomaterials 13, 1187 (2023).
[4] Zollner, Faria Junior, Fabian, PRB (Editors' Suggestion) 100, 085128 (2019); PRB
107, 035112 (2023).
[5] Zollner, Faria Junior, Fabian, PRB 101, 085112 (2020).