▎ 摘　　要

The ill-defined Chern number and disappearing topological edge states make it difficult to characterize the topological properties of a metal. In this work, we investigate the abundant topological phases of monolayer graphene, which is sandwiched by asymmetric ferromagnets and irradiated by off-resonant light. In this system, there exist some rarely noticed metal phases, which are spin-valley polarized metal, topological spin metal (TSM), spin half metal, and topological spin half metal (TSHM). Particularly, for the TSM, the subband with spin up or spin down is topological, but the whole state becomes a metal. For the TSHM, a subband with one spin is topological, while the other subband with the opposite spin is insulated, and the whole state is a spin half metal. As a consequence, one topological protected spin current flows on the edge and the other spin propagates in the bulk. Further calculations indicate that the Berry curvatures for the metal phases are nonzero. We propose to probe the topological properties of the metal states with the anomalous Nernst effect. For these topological phases, spin and valley splitting and flip can be obtained by modulating the Fermi level. An electrically or magnetically controlled switch is designed by a two-terminal TSHM junction. It is expected that these topological metal phases can broaden the band engineering in monolayer graphene and support a promising platform for the studies of spin and valley caloritronics.