Doping a spin-one Mott insulator: possible application to bilayer nickelate

Abstract In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d 8 valence. These studies are particularly relevant—though not limited—to the recently discovered bilayer nickelate superconductor La 3 Ni 2 O 7 . We focus on a ferromagnetic Kondo lattice model with mobile electrons in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> orbital coupled to the localized spin moments in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> orbital through a large Hund’s coupling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mtext>H</mml:mtext> </mml:msub> </mml:mrow> </mml:math> . In the large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mtext>H</mml:mtext> </mml:msub> </mml:mrow> </mml:math> limit, the model reduces to the type II t − J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize density matrix renormalization group results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:mrow> </mml:math> of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> orbital can induce strong inter-layer pairing of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> orbital. In the strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:mrow> </mml:math> limit, a kinetic-energy driven high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:mrow> </mml:math> superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal—dubbed ‘second Fermi liquid (FL)’—in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore presents a promising platform for both realizing higher- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:mrow> </mml:math> superconductors and exploring non-FL physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.