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Magnetic Weyl semimetal in K$_{2}$Mn$_3$(AsO$_{4}$)$_3$ with the minimum number of Weyl points

The "Hydrogen atom" of magnetic Weyl semimetals, with the minimum number of Weyl points, have received growing attention recently due to the possible presence of Weyl-related phenomena. Here, we report a nontrivial electronic structure of the ferromagnetic alluaudite-type compound K$_{2}$Mn$_3$(AsO$_{4}$)$_3$. It exhibits only a pair of Weyl points constrained in the $z$-direction by the two-fold rotation symmetry, leading to extremely long Fermi arc surface states. In addition, the study of its low-energy effective model results in the discovery of various topological superconducting states, such as the "hydrogen atom" of a Weyl superconductor. Our work provides a feasible platform to explore the intrinsic properties related to Weyl points, and the related device applications.