Solitons induced by an in-plane magnetic field in rhombohedral multilayer graphene

We model the influence of an in-plane magnetic field on the orbital motion of electrons in rhombohedral graphene multilayers. For zero field, the low-energy band structure includes a pair of flat bands near zero energy, which are localized on the surface layers of a finite thin film. For finite field, we find that the zero-energy bands persist and that level bifurcations occur at energies determined by the component of the in-plane wave vector q that is parallel to the external field. The occurrence of level bifurcations is explained by invoking semiclassical quantization of the zero-field Fermi surface of rhombohedral graphite. We find parameter regions with a single isoenergetic contour of Berry phase zero corresponding to a conventional Landau level spectrum and regions with two isoenergetic contours, each of Berry phase p, corresponding to a Dirac-like spectrum of levels. We write down an analogous one-dimensional tight-binding model and relate the persistence of the zero-energy bands in large magnetic fields to a soliton texture supporting zero-energy states in the Su-Schrieffer-Heeger model. We show that different states contributing to the zero-energy flat bands in rhombohedral graphene multilayers in a large field, as determined by the wave vector q, are localized on different bulk layers of the system, not just the surfaces.