Four-band effective square-lattice model for Bernal-stacked bilayer graphene

Bernal-stacked bilayer graphene (BLG) provides an ideal basis for\ngate-controlled, and free of etching, electronic devices. Theoretical modeling\nof realistic devices is an essential part of research, however, simulations of\nlarge-scale BLG devices continue to be extremely challenging. Micrometer-sized\nsystems are predominantly beyond the reach of the commonly used atomistic\ntight-binding method, while other numerical approaches based on the two\ndimensional Dirac equation are not straightforward to conduct due to the\nfermion doubling problem. Here we present an approach based on the continuum\nmodel, unharmed by the fermion doubling. The discretization of the BLG\ncontinuum Hamiltonian leads to an effective four-band model, with both valleys\nbuilt-in. We demonstrate its performance with realistic, large-scale systems,\nand obtain results consistent with experiments and with the tight-binding\nmodel, over a broad range of magnetic field.\n