Superconductivity in the spin-state crossover materials: Nickelates with planar-coordinated low-spin Ni2+ ions

We theoretically study quasi-two-dimensional nickel compounds, where the nickel ions assume <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msup><a:mrow><a:mi>Ni</a:mi></a:mrow><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo></a:mrow></a:msup><a:mspace width="4pt"/><a:msup><a:mi>d</a:mi><a:mn>8</a:mn></a:msup></a:mrow></a:math> valence state and feature a low-spin <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>S</c:mi><c:mo>=</c:mo><c:mn>0</c:mn></c:mrow></c:math> ground state quasidegenerate with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>S</d:mi><d:mo>=</d:mo><d:mn>1</d:mn></d:mrow></d:math> ionic excitations. Such a level structure is supported by square-planar coordination of nickel ions or a suitable substitution of apical oxygens. We construct the corresponding singlet-triplet exchange model and explore its phase diagram and excitation spectrum. By hole doping, we further introduce mobile <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><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:mspace width="4pt"/><e:msup><e:mi>d</e:mi><e:mn>7</e:mn></e:msup></e:mrow></e:math> ionic configurations with effective spins <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>S</g:mi><g:mo>=</g:mo><g:mn>1</g:mn><g:mo>/</g:mo><g:mn>2</g:mn></g:mrow></g:math>, and analyze their interactions with the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msup><h:mi>d</h:mi><h:mn>8</h:mn></h:msup></h:math> singlet-triplet background. The interplay with the triplet excitations in the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msup><i:mi>d</i:mi><i:mn>8</i:mn></i:msup></i:math> sector is found to have a deep impact on the propagation of the doped holelike charge carriers and is identified as a powerful source of Cooper pairing among them.