Trends in electronic structures and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>s</mml:mi><mml:mo>±</mml:mo></mml:msub></mml:math>-wave pairing for the rare-earth series in bilayer nickelate superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Ni</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:mrow></mml:math>
Yang Zhang, Ling-Fang Lin, Adriana Moreo, Thomas Maier, Elbio Dagotto
Abstract
The recent discovery of pressure-induced superconductivity in the bilayer ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (LNO) has opened a new platform for the study of unconventional superconductors. In this publication, we investigate theoretically the whole family of bilayer 327-type nickelates ${R}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ ($R$ = rare-earth elements) under pressure. From La to Lu, the lattice constants and volume decrease, leading to enhanced in-plane and out-of-plane hoppings, resulting in an effectively reduced electronic correlation $U/W$. Furthermore, the Ni's ${t}_{2g}$ states shift away from the ${e}_{g}$ states, while the crystal-field splitting between ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ is almost unchanged. In addition, six candidates were found to become stable in the $Fmmm$ phase, with increasing values of critical pressure as the atomic number increases. Similar to the case of LNO, the ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave pairing tendency dominates in all candidates, due to the nesting between the $\mathbf{\text{M}}=(\ensuremath{\pi},\ensuremath{\pi})$ and the $\mathbf{\text{X}}=(\ensuremath{\pi},0)$ and $\mathbf{\text{Y}}=(0,\ensuremath{\pi})$ points in the Brillouin zone. Then, ${T}_{c}$ is expected to decrease as the radius of rare-earth (RE) ions decreases. Our results suggest that LNO is already the ``optimal'' candidate, with Ce a close competitor, among the whole of the RE bilayer nickelates, and to increase ${T}_{c}$ we suggest growing on special substrates with larger in-plane lattice spacings.