Topological Domain Walls in Graphene Nanoribbons with Carrier Doping

We present a theory for the magnetic ground states in doped zigzag graphene nanoribbons (ZGNRs) and clarify the topological origin of their domain wall structure. It is theoretically known that non-interacting ZGNRs have edge states with flat dispersion relation and the electron-electron interaction induces a magnetic order [1,2]. Here we examine the effect of carrier dope on the magnetic structure in terms of the Hartree-Fock mean-field approach. In the low carrier density regime, we observe that magnetic domains with alternating magnetic order is spontaneously formed consistently with Ref. [3]. We analytically demonstrate that the domain-wall bound states are topologically protected by the winding number defined in an effective continuum model. In increasing the doped carrier densities, the distance between the periodically aligned domain walls becomes smaller, and magnetic domain structure crosses over to the spin and charge density wave. We also find that the electronic spectrum as a function of carrier density exhibits a fractal pattern like the Hofstadter butterfly, due to competition of the periodic magnetic structure and atomic lattice.

[1] M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996).

[2] Y.-W. Son, M. L. Cohen, and S. G. Louie, Nature 444, 347 (2006).

[3] M. P. L’opez-Sancho and L. Brey, 2D Materials 5, 015026 (2017).