Abstract
We study the band structure topology and engineering from the interplay between local moments and itinerant electrons in the context of pyrochlore iridates. For the metallic iridate Pr$_2$Ir$_2$O$_7$, the Ir $5d$ conduction electrons interact with the Pr $4f$ local moments via the $f$-$d$ exchange. While the Ir electrons form a Luttinger semimetal, the Pr moments can be tuned into an ordered spin ice with a finite ordering wavevector, dubbed "Melko-Hertog-Gingras" state, by varying Ir and O contents. We point out that the ordered spin ice of the Pr local moments generates an internal magnetic field that reconstructs the band structure of the Luttinger semimetal. Besides the broad existence of Weyl nodes, we predict that the magnetic translation of the "Melko-Hertog-Gingras" state for the Pr moments protects the Dirac band touching at certain time reversal invariant momenta for the Ir conduction electrons. We propose the magnetic fields to control the Pr magnetic structure and thereby indirectly influence the topological and other properties of the Ir electrons. Our prediction may be immediately tested in the ordered Pr$_2$Ir$_2$O$_7$ samples. We expect our work to stimulate a detailed examination of the band structure, magneto-transport, and other properties of Pr$_2$Ir$_2$O$_7$.
Highlights
The study of the electron band-structure topology has attracted a significant attention since the proposal and discovery of topological insulators [1,2,3,4]
We first summarize our understanding of the rich physics in Pr2 Ir2O7 and suggest future experiments to further reveal its physics, and provide a general discussion and vision for hybrid quantum materials of the similar kind
The proximate Ising magnetic order, that is obtained from the condensation of the magnetic monopoles in the Uð1Þ quantum spin liquid, breaks the lattice translation and is precisely the one that is observed in the neutron scattering experiments [36]
Summary
The study of the electron band-structure topology has attracted a significant attention since the proposal and discovery of topological insulators [1,2,3,4]. Resulting valence band develops a nontrivial Chern number and supports a chiral edge state for the quantized Hall transport These two ingredients, i.e., itinerant electrons with a Dirac spectrum and the ferromagnetic local moments, simple on their own, together generate the remarkable phenomenon of the quantum anomalous Hall effect. Theoretical works have considered the long-range Coulomb interaction for the Luttinger semimetal phase of the Ir subsystem [17] These efforts surely fall into the original motivation of searching for correlation physics in strong spin-orbit-coupled matter [8,20] and provide an important understanding of the rich physics in this material. The purpose of our work here is to deviate from the intense efforts on the correlation physics of the Ir subsystems, and is instead to understand the interplay between the Ir conduction electrons and the Pr local moments As it has already been pointed out in Ref. V, we propose various experiments to confirm our prediction and suggest the application and impact to the hybrid quantum materials with both itinerant electrons and local moments
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