Fig. 4

Asymmetric dipolar contributions at the MoS₂/Graphene interface. a, b Induced charge density \(\Delta \rho \left( {10^{ - 4}{\mathrm{e}}{\AA}^{ - 3}} \right)\) (left y-axis) and electric polarization \(\left| {P\left( {10^{ - 3}\,{\mathrm{Cm}}^{ - 2}} \right.} \right|\) (right y-axis) for 1L MoS₂/1L Graphene and 3L MoS₂/3 L Graphene, respectively. The applied electric field is ±1.0 V nm⁻¹. Blue (green) curves correspond to positive (negative) fields. Positive (negative) fields go towards graphene (MoS₂), and vice versa. The MoS₂/Graphene interface is highlighted to show the unbalanced formation of electric dipole moments between graphene and MoS₂ accordingly with the number of layer layers used to form the heterostructures. (c-d) Difference in electrostatic potential \(\Delta V\left( {\mathrm{eV}} \right) = V\left( {E_{{\mathrm{ext}}} \ne 0} \right) - V\left( {E_{{\mathrm{ext}}} = 0} \right)\) in the slabs with and without the external electric field of ±1.0 V nm⁻¹, and their corresponding response field \(\Delta E_\rho \left( {V\;{\mathrm{nm}}^{ - 1}} \right)\) for 1L MoS₂/1L Graphene and 3L MoS₂/3L Graphene, respectively. The absolute values of \(|\Delta E_\rho |\) and \(|\Delta V|\) are taking in (c) and (d) for comparison at the same side of the plot. Geometries for all systems are highlighted at the background of each panel in opacity tone