Tunneling in graphene/h-BN/graphene heterostructures through zero-dimensional levels of defects in h-BN and their use as probes to measure the density of states of graphene

The evolution of the manifestation of levels of defects in h-BN in tunneling through graphene/h-BN/graphene heterostructures with various degrees of perfection, from completely defectless to those with several tens of levels in the band gap of h-BN, has been studied. It has been shown that the behavior of these levels is related to the motion of Dirac points and the chemical potentials of graphene layers at change in the bias and gate voltages, which is described by the electrostatic model of an ideal defectless heterostructure. The density of states of graphene in a magnetic field has been studied by its probing by the level of a single defect with a sensitivity allowing the detection of splitting of the zeroth Landau level caused by the lifting of the spin and valley degeneracy already at $B\sim 4$ T.