▎ 摘　　要

An isolated roughness at the edge of zigzag graphene nanoribbons (zGNRs) breaks the natural bipartite symmetry in the graphene lattice, which might lead to magnetic frustration. Interestingly, the coupling between delocalized states of the roughness and the extended states of the zGNRs induces quantum phenomena, such as destructive quantum interference (DQI), which might play an important role to allow or forbid electrons to transfer through a system. In this work, the electronic and spin-polarized transport properties of the porphine molecule attached to the 6zGNR via different beta- and meso- connections are studied using nonequilibrium Green's function calculations performed within the density functional theory framework (NEGF-DFT). Here, we demonstrated that the porphine/6zGNRs present in the FM ground state for all the couplings and the hybridization between porphine and 6zGNR disturb the bipartite graphene lattice, leading to spin-frustration. Particularly, the porphine molecule introduces Fano-antiresonances in the transmission spectrum that can be controlled by application of a gate voltage (V-g) over the energy position, generating spin filter devices with a high degree of spin polarization of almost 98%. At low bias, the current voltage (I-V-b) characteristics of this system reveal a negative differential resistance (NDR) behavior followed by a flip in spin-current caused by the breaking of symmetry in the scattering region.