Effect of Disorder on Magnetotransport in Semiconductor Artificial Graphene

Abstract

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 $${{R}_{{xy}}}(B)$$ in the magnetic field range of B = 10–50 mT has a hole plateau $${{R}_{{xy}}} = - {{R}_{0}}$$, where R0 = h/2e2 = 12.9 kΩ, at carrier densities in the lattice below the Dirac point n < n1D and an electron plateau $${{R}_{{xy}}} = {{R}_{0}}$$ 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.