We report on high-field magnetotransport (B up to 35 T) on a gated superlattice based on single-layer graphene aligned on top of hexagonal boron nitride. The large-period moiré modulation (≈15 nm) enables us to access the Hofstadter spectrum in the vicinity of and above one flux quantum per superlattice unit cell (Φ/Φ0=1 at B=22 T). We thereby reveal, in addition to the spin-valley antiferromagnet at ν=0, two insulating states developing in positive and negative effective magnetic fields from the main ν=1 and ν=−2 quantum Hall states, respectively. We investigate the field dependence of the energy gaps associated with these insulating states, which we quantify from the temperature-activated peak resistance. Referring to a simple model of local Landau quantization of third-generation Dirac fermions arising at Φ/Φ0=1, we describe the different microscopic origins of the insulating states and experimentally determine the energy-momentum dispersion of the emergent gapped Dirac quasiparticles.
Using the Landau-Zener-Stuckelberg-Majorana-type (LZSM) semiclassical approach, we study both graphene and a thin film of aWeyl semimetal subjected to a strong ac electromagnetic field. The spectrum of quasienergies in the Weyl semimetal turns out to be similar to that of a graphene sheet. It has been predicted qualitatively that the transport properties of strongly irradiated graphene oscillate as a function of the radiation intensity [S. V. Syzranov et al., Phys. Rev. B 88, 241112 (2013)]. Here we obtain rigorous quantitative results for a driven linear conductance of graphene and a thin film of a Weyl semimetal. The exact quantitative structure of oscillations exhibits two contributions. The first one is a manifestation of the Ramsauer-Townsend effect, while the second contribution is a consequence of the LZSM interference defining the spectrum of quasienergies.