Multiband mean-field theory of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:math> superconductivity scenario in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>
Andrew C. Yuan, Erez Berg, Steven A. Kivelson
Abstract
Many seemingly contradictory experimental findings concerning the superconducting state in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the $({D}_{4h})$ symmetry of the crystal: a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave $({B}_{1g})$ and a ${g}_{xy({x}^{2}\ensuremath{-}{y}^{2})}$-wave $({A}_{2g})$ superconducting state. In this paper, we propose a generic multiband model in which the $g$-wave pairing involving the $xz$ and $yz$ orbitals arises from second-nearest-neighbor BCS channel effective interactions. Even if time-reversal symmetry is broken in a $d+ig$ state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature ${T}_{c}$ and the time-reversal symmetry-breaking temperature ${T}_{\text{TRSB}}$ that is qualitatively similar to some of the experimental observations in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$.