Flat-band Lieb electride with emergent quantum phase transitions and superconductivity

The Lieb lattice, characterized by its distinctive Dirac-cone and flat-band electronic structures, hosts a variety of exotic physical phenomena. However, its realization remains largely confined to artificial lattices. In this work, we propose the concept of a Lieb electride, wherein the non-bound electrons gather at the middle edges, behaving as the quasiatoms of a Lieb lattice, enabling the emergence of flat bands. Using crystal structure prediction method MAGUS and first-principles calculations, we predict a stable candidate, Ca₂I, at ambient pressure. Distinct from conventional electrides with localized electrons at cavity centers, Ca₂I features interstitial electrons situated at cavity edges. The resultant flat bands lie close to the Fermi level, giving rise to a pronounced peak in the density of states and leading to Stoner-type ferromagnetism. With increasing pressures, we observe quantum phase transitions from ferromagnetic to non-magnetic and finally to anti-ferromagnetic orders in Ca₂I. Intriguingly, superconductivity emerges in the antiferromagnetic region, suggesting potential competition between these correlated states. Our study not only extend the concepts of electrides but also provide a novel strategy for realizing Lieb lattices through non-bound electrons. This work establishes Ca₂I as a promising platform for exploring flat-band physics and correlated electronic states, opening avenues for novel quantum phenomena in electride-based materials.