Interplay of orbital hopping and perpendicular magnetic field in anisotropic phase transitions for Bernal bilayer graphene and hexagonal boron-nitride.

We theoretically address the perpendicular magnetic field effects on the electronic phase of Bernal bilayer graphene and hexagonal boron-nitride (h-BN) taking into account the total and orbital-projected electronic bands using the tight-binding parameters in the Harrison model, followed by the Green's function method. First, we confirm that our model is computationally efficient and accurate for calculating the magneto-orbital electronic phase transition by reproducing the semimetallic and insulating treatments of pristine Bernal bilayer graphene and h-BN, respectively. In our model, the magnetic field couples only to the electron spin degrees of freedom (with the same contributions for spin-up and spin-down) due to the low dimension of the systems. Here, the main features of the phase transitions are characterized by the electronic density of states (DOS). We found that sp2-hybridization is destroyed when the systems are immersed in the magnetic field, leading to a phase transition to metal for both systems at strong magnetic fields. While there is no phase transition for bilayer graphene at weak magnetic fields, for the case of bilayer h-BN, an insulator to semiconductor phase transition can be viewed, making h-BN more applicable in industry. In bilayer graphene, the anisotropic phase transition appears as insulator-semiconductor, insulator-metal, and semimetal-metal for s-, {px + py}-, and pz-orbitals, respectively, whereas in the case of bilayer h-BN, one observes the same transitions for {s,pz}-orbitals but insulator-semiconductor for {px + py} orbitals. Generically, our findings highlight that the applied magnetic field manipulates the band structure of bilayer graphene and h-BN, and gives ideas to experimentalists for tuning the electro-optical properties of these materials.