Turning copper metal into a Weyl semimetal

Abstract

A search for new topological quantum systems is challenging due to the requirement of nontrivial band connectivity that leads to protected surface states of electrons. Progress in this field was primarily due to a realization of a band inversion mechanism between even and odd parity states that was proven to be very useful in both predicting many such systems and our understanding of their topological properties. Despite many proposed materials that assume the band inversion between $s$ and $p$ (or $p/d$, $d$/$f$) electrons, here, we explore a different mechanism where the occupied $d$ states subjected to a tetrahedral crystal field produce an active ${t}_{2g}$ manifold behaving as a state with an effective orbital momentum equal to $\ensuremath{-}1$, and pushing ${j}_{\mathrm{eff}}=1/2$ doublet at a higher energy. Via hybridization with nearest-neighbor orbitals realizable, e.g., in a zinc-blende structural environment, this allows a formation of odd parity state whose subsequent band inversion with an unoccupied $s$ band becomes possible, prompting us to look for the compounds with ${\mathrm{Cu}}^{+1}$ ionic state. Chemical valence arguments coupled to a search in the materials database of zinc-blende-like lattice space groups ${T}_{d}^{2}$ ($F\overline{4}3m$) lead us to systematically investigate electronic structures and topological properties of CuY ($Y=\text{F}$, Cl, Br, I) and $\mathrm{Cu}X\mathrm{O}$ ($X=\text{Li}$, Na, K, Rb) families of compounds. Our theoretical results show that CuF displays a behavior characteristic of an ideal Weyl semimetal with 24 Weyl nodes at the bulk Brillouin zone. We also find that other compounds, CuNaO and CuLiO, are the $s\text{\ensuremath{-}}d$ inversion-type topological insulators. Results for their electronic structures and corresponding surfaces states are presented and discussed in the context of their topological properties.