Tuning Landau level gap in bilayer graphene on polar substrates

Abstract

We study the effect of carrier interactions with surface optical phonons on the band properties of graphene bilayers induced by polar substrates within the presence of a magnetic field. Employing an analytical method grounded in Lee-Low-Pines theory, we calculate the Hamiltonian spectrum of the Fröhlich type. Our primary focus is on the examination of the alteration in the band gap within the zero-energy Landau level, arising from the substrate’s polaron effect. This gap assumes significance when utilizing hexagonal boron nitride (h-BN) substrates, manifesting a 50 meV deviation compared to graphene sheet. The present work reports the tunability of the energy gap by manipulating substrate polarization and controlling the separation distance between the graphene bilayer and the polar substrate. This tunability is ascribed to the interaction between charge carriers and surface optical phonons, resulting in discernible changes in the band properties of the graphene bilayer.