Prediction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>±</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> -Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>La</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Ni</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> under Pressure
Yang Zhang, Ling-Fang Lin, Adriana Moreo, Thomas Maier, Elbio Dagotto
Abstract
Motivated by the recently reported signatures of superconductivity in trilayer ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$ under pressure, we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals show a bonding-antibonding and nonbonding splitting behavior via the O ${p}_{z}$ orbitals inducing a ``trimer'' lattice in ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$, analogous to the dimers of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$. The Fermi surface consists of three electron sheets with mixed ${e}_{g}$ orbitals, and a hole and an electron pocket made up of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the ${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave channel due to partial nesting between the $\mathbf{M}=(\ensuremath{\pi},\ensuremath{\pi})$ centered pockets and portions of the Fermi surface centered at the $\mathbf{\ensuremath{\Gamma}}=(0,0)$ point. With changing electronic density $n$, the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ instability remains leading and its pairing strength shows a domelike behavior with a maximum around $n=4.2$ ($\ensuremath{\sim}6.7%$ electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-${T}_{c}$ superconductivity of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ does $not$ originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$ with an in-plane ($\ensuremath{\pi}$, $\ensuremath{\pi}$) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.