Emergence of topological phases by stacking of two-dimensional lattices with nonsymmorphic symmetry

Topological semimetals have a variety of phases, whose Fermi surfaces can be nodal points, nodal lines and nodal loops. Here we construct four classes of 3D minimal models via vertically stacking a 2D nonsymmorphic lattice with and without breaking crystalline symmetries. As a result, four distinct topological phases can be generated in our minimal model, such as Dirac nodal line semimetals, Weyl nodal line semimetals, unconventional Weyl semimetals with topological charge [Formula: see text], and weak topological insulators. Unexpectedly, Weyl nodal loops are generated without mirror symmetry protection, where nontrivial 'drumhead' surface states emerge within the loops.