Host: Chaoxing Liu
Although the existence of magnetic monopoles is admitted bythe fundamental laws, the real monopoles in nature remain elusive.Nevertheless, monopoles can appear in realistic condensedmatter systems, from quantum Hall effectsto topologicalsuperconductivity, which spur a race to discover new exotic topological phases of matter. In this talk, we will present dramatic effects arising from topologicalFermi surfaces -- a novel topological class of superconductivity and density-wave orders: Whenthe ordered pairs acquirenon-trivial two-particle Berry phases, their pairing phases cannot bewell-defined globally in the momentum space. Therefore, the conventional description of superconducting pairing symmetries in terms of spherical harmonics (e.g. s-, p-, d-waves) ceases to apply. Instead, they are characterized by topologically protected nodal gap functions represented by monopole harmonic functions. This “monopole harmonic order” is expected to be realized and be detected in Weyl semimetal materials.