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

Abstract

We calculate the electronic band dispersion of graphene monolayer on a two dimensional transition metal dichalcogenide substrate (GTMD) (viz., XY 2 , X = Mo, W; Y = S, Se) around K and K′ 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 XY 2 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 lowlying states strongly suggests the following: The GTMDs like WY 2 exhibit band gap narrowing/widening (Moss-Burstein(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 MoY 2 , 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′ ′ ′ ′. Finally, there is anti-crossing of nonparabolic bands with opposite spins around Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like BiFeO 3 (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.

Strong confinement of unconventional plasmons and optical properties of graphene-transition metal dichalcogenide heterostructures

“…In the lower inset, we have shown the 3D plot of R GTMD for the same Gr-TMD system ( case ignoring the spin-flip scattering events completely. On account of the strong spin-orbit coupling, as already mentioned, the dispersions are gapped at all possible exchange field values with avoided crossings [8].…”

“…It has been also demonstrated ( in I and [8]) that the exchange field can be used for efficient tuning of the band gap, the Thomas-Fermi screening length and the intra-band plasmon frequency. The intra-band conductivity and absorbance, too, can be controlled by the exchange field.…”

“…In this section, for the convenience of the reader, we recall some of the important points in I and [8]. For example, starting with H 0 as in I, we obtain the band dispersion in the form…”

Graphene-TMD Van der Waals Heterostucture Plasmonics

“…In fact, the strong SOCs originate from the d-orbitals of the transition metal atom. The other substrate-driven interactions [5,6,7] (SDIs)correspond to the same sub-lattice transfer of the electronic charge from Gr to TMD leading to a staggered potential gap(G) without spin-flip, and the extrinsic Rashba spin-orbit coupling (RSOC) (ߞ ) that allows for the external tuning of the band gap in Gr-TMD and connects the nearest neighbors with spin-flip. Since the Rashba coupling in graphene is constant for mass-less Dirac electrons and does not depend on the momentum components ( , ) , the intrinsic RSOC, which is modeled as α ( σ x − σ y ) (where σ's are the Pauli matrices) in conventional semiconducting 2D electron gases, have not been considered here.…”