Magnetic-like field inducing negative Dirac mass in graphene on hexagonal boron nitride

•Tight-binding electron in graphene on hexagonal boron nitride is studied.•Electrons behave like relativistic fermions with positive and negative-like masses.•This exotic mass is analogous to that in magnetic-doped topological insulators.•Mass-like magnetic field can cause Larmor precession and Stern–Gerlach magnetic force.

The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force.