Breaking Bipartite and Time Reversal Symmetries by Fusing Porphine Unit in-between two Zigzag-edge Graphene Nanoribbons
Hybrid structure of two zigzag-edge graphene nanoribbons with a fused porphine ring in between, results in two distinct nearly degenerate ground states: a semiconducting antiferromagnetic state and a conducting ferromagnetic state with unequal and opposite Fermi velocities of majority and minority spins, the former having slightly higher stability. Such ground states result from the broken bipartite symmetry induced by the porphine ring. The incorporation of different transition metal atoms in the porphine cavity reduces their energy difference but keeps their electronic properties mostly unchanged. The splitting of the $d$-orbitals in the distorted square-planar ligand field of porphine produces a high spin ground state that breaks the global time reversal symmetry ($\mathcal{T}$). The opposite Fermi velocities of the majority and minority spins in the ferromagnetic ground state and lower sensitivity of the conducting majority spin channel to the edge disorder, make this class of quasi-one-dimensional hybrid structures promising for dual spin-filtering device applications.