Striped spin density wave in a graphene/black phosphorous heterostructure

A bilayer formed by stacking two distinct materials creates a moir\'e lattice, which can serve as a platform for novel electronic phases. In this paper we study a unique example of such a system: the graphene-black phosphorous heterostructure (G/BP), which has been suggested to have an intricate band structure. Most notably, the valence band hosts a quasi-one-dimensional region in the Brillouin zone with high density of states, suggesting that various many-body electronic phases are likely to emerge. We derive an effective tight-binding model that reproduces this band structure, and explore the emergent broken-symmetry phases when interactions are introduced. Employing a mean-field analysis, we find that the favored ground state exhibits a striped spin density wave (SDW) order, characterized by either one of twofold degenerate wave vectors that are tunable by gating. Further exploring the phase diagram controlled by gate voltage and interaction strength, we find that the SDW-ordered state undergoes a metal to insulator transition via an intermediate metallic phase, which supports striped SDW correlations. Possible experimental signatures are discussed, in particular, a highly anisotropic dispersion of the collective excitations, which should be manifested in electric and thermal transport.