Topological nodal semimetals

TLDR

Nodal semimetals feature band touchings at points (Weyl) or lines (line node) in three‑dimensional momentum space. The study investigates the transport properties of nodal semimetals, focusing on quantum‑critical scaling of DC and optical conductivities in Weyl semimetals and graphene‑like behavior in line‑node semimetals. The authors model nodal semimetals by perturbing the normal‑insulator/topological‑insulator critical point with broken time‑reversal symmetry, realizing both Weyl and line‑node states in a NI–TI superlattice. Both Weyl and line‑node semimetals host topologically protected surface states—chiral Fermi arcs in the former yielding finite Hall conductivity, and nearly flat bands in the latter—while exhibiting quantum‑critical scaling of DC and optical conductivities similar to graphene.

Abstract

We present a study of "nodal semimetal" phases, in which non-degenerate conduction and valence bands touch at points (the "Weyl semimetal") or lines (the "line node semimetal") in three-dimensional momentum space. We discuss a general approach to such states by perturbation of the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time reversal (TR) or inversion symmetry. We give an explicit model realization of both types of states in a NI--TI superlattice structure with broken TR symmetry. Both the Weyl and the line-node semimetals are characterized by topologically-protected surface states, although in the line-node case some additional symmetries must be imposed to retain this topological protection. The edge states have the form of "Fermi arcs" in the case of the Weyl semimetal: these are chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. The chiral character of the edge states leads to a finite Hall conductivity. In contrast, the edge states of the line-node semimetal are "flat bands": these states are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone, given by the projection of the line node onto the plane of the edge. We discuss unusual transport properties of the nodal semimetals, and in particular point out 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.