This paper presents a study of nodal semimetal phases, where non-degenerate conduction and valence bands touch at points (Weyl semimetal) or lines (line-node semimetal) in three-dimensional momentum space. The authors 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. They 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 are characterized by topologically-protected surface states. The Weyl semimetal has chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. These edge states lead to a finite Hall conductivity. In contrast, the line-node semimetal has "flat bands" as edge states, which are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone. The paper discusses unusual transport properties of nodal semimetals, including quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal, and similarities to the conductivity of graphene in the line node case. The paper is organized into sections discussing the general theory of perturbed 4-component Dirac points, the point-node (Weyl) semimetal in a TI multilayer, the effect of an orbital field on the Weyl semimetal, the line-node semimetal, and the effect of the orbital part of the field. The authors show that the Weyl semimetal phase exists as long as the separation between the Dirac nodes is within a certain range. The Weyl semimetal is characterized by a finite Hall conductivity and chiral edge states. The line-node semimetal has topologically protected surface states that form a flat band in the surface Brillouin zone. The paper also discusses the stability of the line-node semimetal and the effects of the orbital part of the field on the system. The authors conclude that the line-node semimetal is more robust than the Weyl semimetal and that the topological surface states survive even when the bulk line node is destroyed by a particle-hole asymmetry. The paper provides a detailed analysis of the transport and optical properties of the Weyl and line-node semimetals, highlighting their unique characteristics and potential for experimental study.This paper presents a study of nodal semimetal phases, where non-degenerate conduction and valence bands touch at points (Weyl semimetal) or lines (line-node semimetal) in three-dimensional momentum space. The authors 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. They 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 are characterized by topologically-protected surface states. The Weyl semimetal has chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. These edge states lead to a finite Hall conductivity. In contrast, the line-node semimetal has "flat bands" as edge states, which are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone. The paper discusses unusual transport properties of nodal semimetals, including quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal, and similarities to the conductivity of graphene in the line node case. The paper is organized into sections discussing the general theory of perturbed 4-component Dirac points, the point-node (Weyl) semimetal in a TI multilayer, the effect of an orbital field on the Weyl semimetal, the line-node semimetal, and the effect of the orbital part of the field. The authors show that the Weyl semimetal phase exists as long as the separation between the Dirac nodes is within a certain range. The Weyl semimetal is characterized by a finite Hall conductivity and chiral edge states. The line-node semimetal has topologically protected surface states that form a flat band in the surface Brillouin zone. The paper also discusses the stability of the line-node semimetal and the effects of the orbital part of the field on the system. The authors conclude that the line-node semimetal is more robust than the Weyl semimetal and that the topological surface states survive even when the bulk line node is destroyed by a particle-hole asymmetry. The paper provides a detailed analysis of the transport and optical properties of the Weyl and line-node semimetals, highlighting their unique characteristics and potential for experimental study.