Interlayer pairing in bilayer nickelates

Abstract The discovery of T c ~ 80 K superconductivity in pressurized La 3 Ni 2 O 7 has launched a new platform to study high-temperature superconductivity. Using non-perturbative dynamic cluster approximation quantum Monte Carlo calculations, we characterize the magnetic and superconducting pairing behavior of a realistic bilayer two-orbital Hubbard-Hund model of this system that describes the relevant Ni e g states with physically relevant interaction strengths. We find a leading s ± superconducting instability in this model at a temperature T ~ 100 K close to the experimentally observed T c . Analyzing the orbital and spatial structure of the effective pairing interaction giving rise to this state reveals that the interaction predominantly acts between local interlayer pairs of the $${d}_{3{z}^{2}-{r}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:msup> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> orbital. By correlating the strength of the interaction with that of the magnetic spin fluctuations we show that it is driven by strong interlayer spin-fluctuations arising from the $${d}_{3{z}^{2}-{r}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:msup> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> orbital. These results provide first-time non-perturbative evidence supporting the picture that a simple single-orbital bilayer Hubbard model for the Ni $${d}_{3{z}^{2}-{r}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:msup> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> orbital provides an excellent low-energy effective description of the superconducting behavior of La 3 Ni 2 O 7 .