Wannier diagrams for semiconductor artificial graphene

Quantum transport has been simulated in hexagonal semiconductor lattices of antidots with a period of $80$ nm and short-range disorder. Wannier diagrams, i.e., $DoS(n, B)$ maps of the density of states, where $n$ is the electron density and $B$ is the magnetic field strength, have been calculated for several potential modulation amplitudes comparable to or much larger than the Fermi energy. Deep dips in the maps of the density of states have the form of rays with positive, zero, and negative slopes. In addition to the fan of the rays separating the first and second, as well as the second and third Landau levels, the maps include rays that are parallel to them and are shifted in $n$ and $B$ by integers of the characteristic electron density $n_0$ and the characteristic magnetic field strength $B_0$, respectively. It has been shown that the sign and magnitude of the slope of the rays in the density of states correspond to the centers of the plateaus of quantized Hall resistances $R_{xy}$. The lattice is brightly manifested in the $R_{xy}(n, B)$ maps as the replicas of the first and second plateaus in $R_{xy}$ and as oscillations of $R_{xy}$ between negative and positive values at a fixed magnetic field or a fixed electron density, which indicates the interchange between the hole and electron charge carriers.