Phase Diagram of Nickelate Superconductors Calculated by Dynamical Vertex Approximation
Karsten Held, Liang Si, Paul Worm, Oleg Janson, Ryotaro Arita, Zhicheng Zhong, Jan M. Tomczak, Motoharu Kitatani
Abstract
We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model, we identify the one-band Hubbard model for the Ni 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>x</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>y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:math> orbital plus a pocket around the A -momentum. The latter, however, merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from nominal Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by the experiment, indicate that the Γ pocket, Nd 4 f orbitals, oxygen 2 p , and the other Ni 3 d orbitals are not relevant in the superconducting doping regime. The physics is completely different if topotactic hydrogen is present or the oxygen reduction is incomplete. Then, a two-band physics hosted by the Ni 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>x</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>y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:math> and 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><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> orbitals emerges. Based on our minimal modeling, we calculated the superconducting T c vs. Sr-doping x phase diagram prior to the experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as T c , the agreement with the experiment is astonishingly good. The prediction that T c is enhanced with pressure or compressive strain has been confirmed experimentally as well. This supports that the one-band Hubbard model plus an electron reservoir is the appropriate minimal model.