Proximity effects constitute a highly promising tool for versatile engineering of the band structure of graphene in van der Waals  heterostructures [1]. Particularly promising relevant systems are based  on transition metal dichalcogenides [2]. In the paper some approaches to  tune the proximity effects in reversible manner will be discussed. A  main one is based on charge density wave degree of freedom. Such a  low-temperature ordering is known to develop in 1T polytypes of TaS2 and  NbS2, enabling to manipulate the band structure of heterostructures in twistronic-like way without physical alteration of the twist angle.

In the paper the DFT calculations-based predictions of proximity  effects in graphene band structure emerging in heterostructures with  TaS2 [3] and NbS2 and controllable with charge density wave ordering  will be presented. Moreover, magnetism in TaS2 [4] will be discussed as  yet another mechanism capable of shaping the proximity effects. Also the  external electric field will be demonstrated to be an additional useful  factor influencing the band structure.

The interpretation of the results will be based on symmetry-based  tight-binding Hamiltonians [3]. Special emphasis will be put on  proximity-induced Rashba spin-orbit coupling parametrized by  characteristic energy and tuneable angle (inducing possible anisotropic  Rashba-Edelstein effect).

Acknowledgements: Financial support provided by the University of Łódź  under Grant No. 1/IDUB/DOS/2021 is gratefully acknowledged. Polish  high-performance computing infrastructure PLGrid (HPC Centers: ACK  Cyfronet AGH) is gratefully acknowledged for providing computer  facilities and support within computational grant no. PLG/2023/016571.

[1]  J. F. Sierra, J. Fabian, R. K. Kawakami, S. Roche and S. O.  Valenzuela,  Nature Nanotechnology 16, 856 (2021)
[2] M. Gmitra and J. Fabian,  Physical Review B 92, 155403 (2015)
[3] K. Szałowski, M. Milivojević, D. Kochan and M. Gmitra, 2D Materials 10, 025013 (2023)
[4] I. Lutsyk, K. Szałowski et al., Nano Research 16, 11528 (2023)