Monopole Superconductivity and Density-Wave Order in Weyl Semi-metals

We introduce a novel topological class of superconducting and density-wave states which exhibit monopole harmonic symmetry. This so-called “monopole harmonic order” can be realized in interacting Weyl semimetal materials. Generally, when two Fermi surfaces carry different Chern numbers, the many-body ordering between these two Fermi surfaces can exhibit a non-trivial Berry phase inherited from band structure topology. In contrast to other known many-body order, the total vorticity of the ordering gap nodes in momentum space is determined by the monopole charge of the pair Berry phase and is independent of specific ordering mechanisms. Connections to experimental realizations and signatures of monopole harmonic superconductivity and monopole harmonic charge-density-wave states are proposed.

1. Yi Li and Haldane, “Topological Nodal Cooper Pairing in Doped Weyl Metals”, Phys. Rev. Lett. 120, 067003 (2018);
2. Eric Bobrow, Canon Sun, and Yi Li, “Monopole Charge Density Wave States in Weyl Semimetals”, arXiv: 1810.08715.