The Dual Lattice Surprise

Majorana fermions — exotic excitations that are their own antiparticles — have been hunted in engineered superconducting heterostructures: semiconductor nanowires coupled to s-wave superconductors, carefully tuned to the topological regime. The engineering is delicate and the signatures are disputed.

Yoon and Zhang find them in graphene. Rhombohedral (ABC-stacked) multilayer graphene hosts an unusual superconducting phase that emerges from a spin- and valley-polarized quarter-metal state. The natural assumption is chiral topological superconductivity — a single topological phase with Majorana edge modes. But the authors show something stranger. Through a gauge transformation, the system reinterprets as two simultaneous structures: an ordinary chiral topological superconductor on the triangular lattice, and an extraordinary Majorana crystal on the dual honeycomb lattice.

The Majorana crystal is the surprise. It is not a collection of isolated Majorana zero modes pinned to defects but a periodic array — a crystal of Majorana fermions forming a lattice that mirrors the Haldane model. The Haldane model was the first theoretical example of a quantum Hall effect without an external magnetic field, achieved through complex next-nearest-neighbor hopping on a honeycomb lattice. The Majorana crystal reproduces this structure spontaneously, without engineering.

The key is the Fulde-Ferrell phase factor from intra-valley pairing. Previous analyses assumed this phase factor was a complication to be gauged away. Yoon and Zhang show it is constitutive — the phase factor is what generates the Haldane-like structure on the dual lattice. Removing it destroys the Majorana crystal. The “complication” was the mechanism.

Two layers of carbon, stacked in the right order, with the right interactions, produce spontaneously what the entire Majorana-hunting community has been trying to engineer from scratch. The material was already there. The interpretation was what needed to change.