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Effect of ferromagnetic exchange field on band-gap and spin-polarization of graphene on a TMD substrate

We calculate the electronic band dispersion of graphene monolayer on a two dimensional transition metal dichalcogenide substrate (GTMD) (viz., XY2 , X = Mo, W; Y = S, Se) around K and K prime points taking into account the interplay of the exchange field due to the ferromagnetic impurities and the substrate induced, sub-lattice-resolved, strongly enhanced intrinsic spin-orbit couplings(SOC). There are extrinsic Rashba spin-orbit coupling(RSOC) and the orbital gap related to the transfer of the electronic charge from graphene to XY2 as well. The former allows for external tuning of the band gap in GTMD and connects the nearest neighbors with spin-flip. On account of the strong SOC, the system acts as a quantum spin Hall insulator. We introduce the exchange field (M) in the Hamiltonian to take into account the deposition of Fe atoms on the graphene surface. The cavalcade of the perturbations yield particle-hole symmetric bands with an effective Zeeman field due to the interplay of the substrate induced interactions with RSOC as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GTMDs like WY2 exhibit band gap narrowing/widening (Moss-Burs-tein(MB)gap shift)including the spin-polarization inversion(SPI) at finite but low temperature (T = 1 K) due to the increase in the exchange field (M) at the Dirac point K. For graphene on MoY2, on the other hand, the occurrence of the MB-shift and the SPI at higher temperature (T = 10 K) take place as M is increased at the Dirac point K prime. Finally, there is anti-crossing of non-parabolic bands with opposite spins around Dirac points. A direct electric field control of magnetism at the nano-scale is needed here. The magnetic multi-ferroics, like BiFeO3 (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.