Temperature effect of tunable zero Landau Level splitting energy of monolayer graphene on substrates

The temperature effects of the tunable zero-Landau lever (LL) energy are studied using the Lee-Low-Pines (LLP) variational and quantum statistical theory in the presence of a magnetic field B on monolayer graphene of different polar substrates. This zero-LL energy was induced by the surface optical phonon polaron in monolayer graphene on polar substrates. We found that zero-LL splitting energy can be tuned by controlling the polarization strength ηof the polar substrate, confinement strength parameter g, magnetic field B, and temperature T. The magnetic field has a negligible impact on the zero-LL splitting energy. And the temperature effect of zero-LL splitting energy of graphene substrates is further enhanced by Coulomb potential. The results obtained in the study provide new information about the fundamental properties of graphene on substrates at different temperatures T.