Orbital-Selective Diagonal-Gap Test of Pairing in La${}_3$Ni${}_2$O${}_7$

Abstract

Recent angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) measurements on bilayer nickelate La${}_3$Ni${}_2$O${}_7$ reveal a nearly isotropic, nodeless superconducting gap. We show that these single-particle spectra provide a symmetry-enforced test of the pairing nature. Mirror symmetry forces the hybridization between $d_{z^2}$ and $d_{x^2-y^2}$ orbitals to vanish along the Brillouin-zone (BZ) diagonal. Consequently, the gaps on the diagonal portions of the $\alpha /\beta$ and $\gamma$ Fermi pockets separately probe the intrinsic pairing strengths of the $d_{x^2-y^2}$ and $d_{z^2}$ sectors. A pairing state with pure or dominant intrinsic $d_{z^2}$-orbital pairing component produces nodes or near-nodes on the BZ diagonal of the $\alpha /\beta$ pockets and is thus challenged by ARPES and STM, whereas the pairing state with dominant intrinsic $d_{x^2-y^2}$-orbital pairing component has a nearly isotropic, nodeless gap on all pockets which well fits ARPES and STM data. The dominant $d_{x^2-y^2}$-orbital pairing is compatible with Hund's-rule-driven pairing mechanisms.

4.1 pages, 4 figures, with Appendix