Dirac fermions and pseudomagnetic fields in two-dimensional electron gases with triangular antidot lattices

Abstract

We investigate theoretically the electronic properties of two-dimensional electron gases (2DEGs) with regular and distorted triangular antidot lattices. We show that the triangular antidot lattices embedded in 2DEGs behave like artificial graphene and host Dirac fermions. By introducing the Wannier representation, we obtain a tight-binding Hamiltonian including the second-nearest-neighboring hopping, which agrees well with the numerically exact solutions. Based on the tight-binding model, we find that spatially nonuniform distortions of the antidot lattices strongly modify the electronic structures, generate pseudomagnetic fields and the well-defined Landau levels. In contrast to graphene, we can design the nonuniform distortions to generate various configurations of pseudomagnetic fields. We show that the snake orbital states arise by designing the $\ifmmode\pm\else\textpm\fi{}\mathbf{B}$ pseudomagnetic field configuration. We find that the disorders of antidot lattices during fabrication would not affect the basic feature of the Dirac electrons, but they lead to a reduction in conductance in strong disorder cases.