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

摘要

We calculate the electronic band dispersion of graphene monolayer on a two-dimensional transition metal dichalcogenide substrate (GrTMD) around $f{K}$ and $f{K'}$ points by taking into account the interplay of the ferromagnetic impurities and the substrate-induced interactions. The latter are (strongly enhanced) intrinsic spina??orbit interaction (SOI), the extrinsic Rashba spina??orbit interaction (RSOI) and the one related to the transfer of the electronic charge from graphene to substrate. We introduce exchange field $(M)$ in the Hamiltonian to take into account the deposition of magnetic impurities on the graphene surface. The cavalcade of the perturbations yield particlea??hole symmetric band dispersion with an effective Zeeman field due to the interplay of the substrate-induced interactions with RSOI as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GrTMDs, such as graphene on $m{WY_2}$, exhibit (direct) band-gap narrowing/widening (Mossa??Burstein (MB) gap shift) including the increase in spin polarisation $(P)$ at low temperature due to the increase in the exchange field $(M)$ at the Dirac points. The polarisation is found to be electric field tunable as well. Finally, there is anticrossing of non-parabolic bands with opposite spins, the gap closing with same spins, etc. around the Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like $m{BiFeO_{3}}$ (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.