Detecting pairing symmetry of bilayer nickelates using electronic Raman scattering

Abstract: The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates La$3$Ni$_2$O$_7$ has garnered significant attention. However, the corresponding pairing symmetry remains debated in both experiments and theoretical studies due to conflicting experimental evidence from bulk and thin-film materials. In this work, we examine the electronic Raman response across different channels for various pairing symmetries within a two-orbital bilayer model. By comparing Raman susceptibilities obtained from multiorbital and band-additive approaches, we demonstrate that Raman response can distinguish between different pairing symmetries and identify pocket-dependent gap amplitudes for both fully gapped and nodal superconducting states. Specifically, the nodal $d{x^2-y^2}/d_{xy}$-wave pairing exhibits robust low-energy power-law behavior, distinct from a fully gapped pairing. Additionally, for the $s_{\pm}$-wave pairing, the detailed gap anisotropy on the $β$ pocket can be determined. Possible experimental implications are also discussed. Our results highlight the crucial role of multiorbital effects in shaping the Raman spectra and establish electronic Raman scattering as a powerful and symmetry-resolved probe for determining the superconducting gap in unconventional superconductors.