Extreme structure and spontaneous lift of spin degeneracy in doped perforated bilayer graphenes

Extreme structure and spin states of doped and undoped perforated bigraphenes was studied using DFT simulations. It was found that folded nanopores possess extremely high curvature of 0.34 Å⁻¹. Dramatic structural deformation causes severe changes of the chemical properties of carbon atoms localized at the nanopores converting the folded edges to local oxidative fragments. It was found that asymmetrical coordination of either Li, Ca, or Al to the nanopores is coupled with electron transfer from metal to edge carbon atoms and breakdown of local inversion symmetry. Li-, Ca-, and Al-doped perforated AA bigraphene revealed ferromagnetic spin ordering with magnetic moments of 0.38, 0.14, and 0.32μ_B/unit cell, respectively, and spin polarization energy gain of 0.037eV for Ca-doped superlattice. It was shown that ferromagnetic spin ordering of bigraphene nanopores contradicts to the Nagaoka's theorem, which excludes strong electron correlations as a reason of spin polarization. Spontaneous lift of spin degeneracy was interpreted in terms of perturbing intense local electrostatic fields from extra electron charges localized at the nanopore edges, coupled with breakdown of space inversion and local translation invariances. It was shown that spin energy splitting is proportional to the matrix elements calculated on Bloch states with opposite wavevectors and perturbing electrostatic fields.