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 μm, 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 
 in the magnetic field range of B = 10–50 mT has a hole plateau 
, where R0 = h/2e2 = 12.9 kΩ, at carrier densities in the lattice below the Dirac point n < n1D and an electron plateau 
 at n > n1D. 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.