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Realizing controllable room-temperature ferromagnetism in carbon-based materials is one of recent prospects. The magnetism in graphene nanostructures reported previously is mostly localized by breaking the local sublattice imbalance. Here, we predict a robustly potential-tuned ferromagnetic domain lying between the inter-chain carbon atoms inside the zigzag graphene nanoribbons. We show that the effective zigzag edges provide the strong correlation background through narrowing the band width, while the internal Van Hove filling (VHF) provides the strong ferromagnetic background inherited from the bulk. The induced ferromagnetism exhibit interesting switching effect when the nominal VHF crosses the intra- and inter-chain region by tuning the potential drops. We further observe a robust half-metallicity transition from one spin channel to another within the same magnetic phase. These novel properties provide promising ways to manipulate the spin degree of freedom in graphene nanostructures.

Symmetry of superconducting pairing is one of the cardinal issues in superconductivity. In general, the nearest-neighbor and next-nearest-neighbor pairings cannot spontaneously mix with each other constrained by the distinct symmetry classification, for example the ${d}_{{x}^{2}-{y}^{2}}$ - and d _xy -wave pairings in the square lattice. The honeycomb lattice provides a special platform to study the mixture of the nearest-neighbor and the next-nearest-neighbor pairing components due to its unique crystal structure. Here, using the variational quantum Monte Carlo simulations, we report a robust superconducting ground state with the intrinsic mixture of the nearest-neighbor and next-nearest-neighbor chiral d + id -wave pairings on the honeycomb lattice. We numerically identify that the two pairing channels promote each other. The proportion of the next-nearest-neighbor d + id component can be readily tuned by doping density and the short-range interactions. Our results provide the efficient ways to manipulate the real-space pairings.

The possible ground states of the undoped and doped Kitaev–Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases, including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated using the Schwinger-fermion mean-field method, and we obtain an energetically favorable Z _2 chiral spin liquid with a Chern number ±2 as a promising candidate. At finite doping, we find that the AF Heisenberg coupling supports an s -wave or a ${{d}_{{{x}^{2}}-{{y}^{2}}}}+{\rm i}{{d}_{xy}}$ -wave superconductivity (SC), while the AF and the ferromagnetic Kitaev interactions favor a ${{d}_{{{x}^{2}}-{{y}^{2}}}}+{\rm i}{{d}_{xy}}$ -wave SC and a time-reversal invariant topological p -wave SC, respectively. Possible experimental realizations and related candidate materials are also discussed.