Orbital order and superconductivity in bilayer nickelate compounds

We propose a theory for bilayer nickelate materials, where a large tetragonal field—intrinsic or induced by epitaxial strain—lifts the orbital degeneracy and localizes the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>3</a:mn> <a:msup> <a:mi>z</a:mi> <a:mn>2</a:mn> </a:msup> <a:mo>−</a:mo> <a:msup> <a:mi>r</a:mi> <a:mn>2</a:mn> </a:msup> </a:mrow> </a:math> orbital states. These states host local spins <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>S</b:mi> <b:mo>=</b:mo> <b:mn>1</b:mn> <b:mo>/</b:mo> <b:mn>2</b:mn> </b:mrow> </b:math> bound into singlets by strong interlayer coupling, and their dynamics is described by weakly dispersive singlet-triplet excitations (“triplons”). The charge carriers occupy the wide bands of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mi>x</c:mi> <c:mn>2</c:mn> </c:msup> <c:mo>−</c:mo> <c:msup> <c:mi>y</c:mi> <c:mn>2</c:mn> </c:msup> </c:mrow> </c:math> symmetry, and their Cooper pairing is mediated by the high-energy triplon excitations. As the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msup> <d:mi>x</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo>−</d:mo> <d:msup> <d:mi>y</d:mi> <d:mn>2</d:mn> </d:msup> </d:mrow> </d:math> band filling increases, i.e., moving further away from the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msup> <e:mrow> <e:mi>Ni</e:mi> </e:mrow> <e:mrow> <e:mn>3</e:mn> <e:mo>+</e:mo> </e:mrow> </e:msup> </e:math> valence state, the indirect Ruderman-Kittel-Kasuya-Yosida interactions between local spins induce spin-density-wave order via triplon condensation. Implications of the model for compressively strained <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>La</f:mi> <f:mn>3</f:mn> </f:msub> <f:msub> <f:mi>Ni</f:mi> <f:mn>2</f:mn> </f:msub> <f:msub> <f:mi mathvariant="normal">O</f:mi> <f:mn>7</f:mn> </f:msub> </f:mrow> </f:math> films and electron-doped oxychloride <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>Sr</h:mi> <h:mn>3</h:mn> </h:msub> <h:msub> <h:mi>Ni</h:mi> <h:mn>2</h:mn> </h:msub> <h:msub> <h:mi mathvariant="normal">O</h:mi> <h:mn>5</h:mn> </h:msub> <h:msub> <h:mi>Cl</h:mi> <h:mn>2</h:mn> </h:msub> </h:mrow> </h:math> are discussed.