▎ 摘　　要

Graphene spirals (GSs), an emerging carbonic nano-material with a Riemann surface, demonstrate extraordinary topological electronic signatures: interlayer coupling similar to van der Waals (vdW) heterojunctions and intralayer coupling within the spiral conformation. Based on the state-of-the-art first-principles technique, the electronic properties of the periphery-modified GSs with geometry deformation are explored under axial strain. For all GSs, there emerges a remarkable phase transition from metal to semiconductor, due to the attenuation of interlayer "sigma-bonds" reducing the interlayer tunneling probability for carriers. Analogous to graphene, GSs consist of bipartite sublattices with carbonic sp(2) hybridization as well. Once the balance of the bipartite sublattices is lost, there will emerge intense edge (corner) states, contributed by the p(z) orbitals. In contrast to isolated graphene nanoflakes, GSs realize the continuous spin-polarized edge (corner) state coupling with 1D morphology. However, the spin-polarization is blocked by the robust interlayer "sigma-bonds" so that the spintronic transition takes place until this interlayer coupling is broken. More intriguingly, an indirect-direct bandgap transition is observed, revealing excellent optical on-off features. Their tunable properties provide great potential for their application in optoelectronics, spintronics and chemical or biological sensors.