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Young and Kane have given a great insight for 2D Dirac semimetals withnontrivial topology in the presence of nonsymmorphic crystalline symmetry.Based on one of 2D nonsymmorphic square lattice structures they proposed, wefurther construct a set of 3D minimal tight-binding models via verticallystacking the 2D nonsymmorphic lattice. Specifically, our model provides aplatform to generate three topologically semimetallic phases such as Diracnodal line semimetals, Weyl nodal line semimetals and Weyl semimetals. Theoff-centered mirror symmetry sufficiently protects nodal lines emerging withinmirror-invariant plane with a nontrivial mirror invariant $n_{M\mathbb{Z}}$,whereas twofold screw rotational symmetry protects nontrivial Weyl nodal pointswith topological charge $C=2$. Interestingly, Weyl nodal loops are generatedwithout mirror symmetry protection, where nontrivial "drumhead" surface statesemerge within loops. In the presence of both time-reversal and inversionsymmetries, the emergence of weak topological insulator phases is discussed aswell.

Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetries