Fig. 3

Motion of Weyl points and Fermi arcs in an effective 3D model. A 4D nodal loop (NL) system can be viewed as an effective 3D nodal point system with an extra parameter. Each of (a–e) is a 2D “slice" of Fig. 2e, with \({k}_{y}^{{\prime} }={k}_{y}+{k}_{z}\), \({k}_{z}^{{\prime} }={k}_{y}-{k}_{z}\), and \({k}_{y}^{{\prime} }\) taken as a parameter describing the additional fourth dimension. Here \({k}_{x,y,z}\) represent the quasi-momenta of the 3D boundary Brilloun zone of a 4D system with open boundary conditions along \(\hat{w}\) direction. The red points/blue lines correspond to the intersecting region of the nodal loops/Seifert surface states and the slices, analogous to the Weyl points/Fermi arcs in an effective 3D Weyl semimetal, with the two quasi-momenta of its 2D boundary Brillouin zone given by \({k}_{x}\) and \(k^{\prime}\). The arrows show the movement of the Weyl points when increasing \({k}_{y}^{^{\prime} }\). The chirality of the Weyl points is shown by the plus or minus signs in the figure