Coexistence of Van Hove Singularities and Pseudomagnetic Fields in Modulated Graphene Bilayer

Abstract: The stacking and bending of graphene are trivial but extremely powerful agents of control over graphene's manifold physics. By changing the twist angle, one can drive the system over a plethora of exotic states via strong electron correlation, thanks to the moir\'e superlattice potentials, while the periodic or triaxial strains induce discretization of the band structure into Landau levels without the need for an external magnetic field. We fabricated a hybrid system comprising both the stacking and bending tuning knobs. We have grown the graphene monolayers by chemical vapor deposition, using $^{12}$C and $^{13}$C precursors, which enabled us to individually address the layers through Raman spectroscopy mapping. We achieved the long-range spatial modulation by sculpturing the top layer ($^{13}$C) over uniform magnetic nanoparticles (NPs) deposited on the bottom layer ($^{12}$C). An atomic force microscopy study revealed that the top layer tends to relax into pyramidal corrugations with C$_3$ axial symmetry at the position of the NPs, which have been widely reported as a source of large pseudomagnetic fields (PMFs) in graphene monolayers. The modulated graphene bilayer (MGBL) also contains a few micrometer large domains, with the twist angle ~ 10$^{\circ}$, which were identified via extreme enhancement of the Raman intensity of the G-mode due to formation of Van Hove singularities (VHSs). We thereby conclude that the twist induced VHSs coexist with the PMFs generated in the strained pyramidal objects without mutual disturbance. The graphene bilayer modulated with magnetic NPs is a non-trivial hybrid system that accommodates features of twist induced VHSs and PMFs in environs of giant classical spins.