Stacking graphene on monolayer black phosphorus produces a heterostructure whose hybridised valence band, unlike the isotropic Dirac cone of graphene alone, contains long nearly-flat stretches of energy contour - quasi-one-dimensional regions of the Brillouin zone carrying a very high density of states, which is exactly the condition under which weak repulsive interactions produce a broken-symmetry ground state. This concept covers the full argument from lattice to phase diagram: a four-site tight-binding model of black phosphorus as coupled zigzag chains with intra-layer and inter-layer hopping, its hybridisation with graphene's lower Dirac cone once charge transfer raises the phosphorus valence band toward the Fermi level, an effective continuum reduction of the resulting upper valence band, and then a mean-field treatment of on-site repulsion with competing spin-density-wave and charge-density-wave order parameters. The spin density wave wins, and it is striped: the ordering wave vector is one of two degenerate choices set by the anisotropic band contour, and gating selects between them. Sweeping gate voltage and interaction strength maps a phase diagram in which the ordered state reaches an insulator not directly but through an intermediate metallic phase that still carries striped correlations. The predicted experimental signature is a strongly anisotropic dispersion of the collective excitations, visible in electrical and thermal transport.
A bilayer formed by stacking two distinct materials creates a moiré lattice, which can serve as a platform for novel electronic phases. In this work we study a unique example of such a system: the gr…