Effect of disorder on magnetotransport in semiconductor artificial graphene

Magnetotransport in mesoscopic samples with semiconductor artificial graphene has been simulated within the Landauer–Büttiker formalism. Model four-terminal systems in a high-mobility two-dimensional electron gas have a square shape with a side of $3$–$5$ $\mu$m, which is filled with a short-period ($120$ nm) weakly disordered triangular lattice of antidots at the modulation amplitude of the electrostatic potential comparable with the Fermi energy. It has been found that the Hall resistance $R_{xy}(B)$ in the magnetic field range of $B=10$–$50$ mT has a hole plateau $R_{xy}=-R_0$, where $R_0=h/2e^2=12.9\, \mathrm{k}\Omega$, at carrier densities in the lattice below the Dirac point $n<n_{1D}$ and an electron plateau $R_{xy}=R_0$ at $n>n_{1D}$. Enhanced disorder destroys the plateaus, but a carrier type (electrons or holes) holds. Long-range disorder at low magnetic fields suppresses quantized resistance plateaus much more efficiently than short-range disorder.