The paper by A.A. Burkov, M.D. Hook, and Leon Balents explores the properties of "nodal semimetal" phases, characterized by non-degenerate conduction and valence bands that touch at points (Weyl semimetal) or lines (line node semimetal) in three-dimensional momentum space. They discuss a general approach to these states by perturbing the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time reversal (TR) or inversion symmetry. The authors provide an explicit model realization of both types of states in a NI-TI superlattice structure with broken TR symmetry. Both the Weyl and line-node semimetals exhibit topologically protected surface states, with the former showing chiral gapless edge states (Fermi arcs) and the latter having flat bands. The edge states of the Weyl semimetal have a finite Hall conductivity, while those of the line-node semimetal are dispersionless in a subset of the two-dimensional edge Brillouin zone. The paper also discusses the unusual transport properties of these nodal semimetals, including quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal and similarities to graphene in the line-node case.The paper by A.A. Burkov, M.D. Hook, and Leon Balents explores the properties of "nodal semimetal" phases, characterized by non-degenerate conduction and valence bands that touch at points (Weyl semimetal) or lines (line node semimetal) in three-dimensional momentum space. They discuss a general approach to these states by perturbing the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time reversal (TR) or inversion symmetry. The authors provide an explicit model realization of both types of states in a NI-TI superlattice structure with broken TR symmetry. Both the Weyl and line-node semimetals exhibit topologically protected surface states, with the former showing chiral gapless edge states (Fermi arcs) and the latter having flat bands. The edge states of the Weyl semimetal have a finite Hall conductivity, while those of the line-node semimetal are dispersionless in a subset of the two-dimensional edge Brillouin zone. The paper also discusses the unusual transport properties of these nodal semimetals, including quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal and similarities to graphene in the line-node case.