Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates

TLDR

The topological semimetal is a three‑dimensional analogue of graphene with linearly dispersing excitations, realizing Weyl fermions and exhibiting Fermi‑arc surface states that cannot occur in purely two‑dimensional band structures. We investigate novel phases that emerge from the interplay of electron correlations and strong spin‑orbit interactions, focusing on the topological semimetal phase. We employ LDA+U calculations to show that the topological semimetal can be realized in pyrochlore iridates such as Y₂Ir₂O₇. For intermediate correlation strengths, the ground state of pyrochlore iridates is the topological semimetal coexisting with noncollinear magnetic order, with a narrow axion‑insulator window and a magnetic‑field‑induced metallic state.

Abstract

We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic ``axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.