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.

Figures (6)

• Figure 1: (a) Electronic structure of La$_3$Ni$_2$O$_7$ under pressure. The orbital-resolved band structure is shown, where colors represent the orbital contributions. The inset displays the Fermi surface obtained from the tight-binding model at filling $n=3$. (b) Normal-state Raman response above the interband transition energy scale. The inset illustrates the crystalline $a$ and $b$ axes, as well as the polarization geometries for the incident and scattered photons in the $B_{1g}$ and $B_{2g}$ channels.
• Figure 2: Superconducting gap on the Fermi surface for four representative pairing states: (a) intralayer-dominated $s_{++}$, (b) interlayer-dominated $s_{\pm}$, (c) in-plane $d_{x^2-y^2}$ pairing, and (d) in-plane $d_{xy}$ pairing.
• Figure 3: The Raman responses in the $A_{1g}$ (a,d), $B_{1g}$ (b,e), and $B_{2g}$ (c,f) channels for the $s_{\pm}/s_{++}$-wave pairing with the gap maximum on $\beta$ pocket along the diagonal direction (a-c) and around X points (d-f), corresponding to Figs. 2(a) and 2(b). The blue solid curves represent the full multiorbital (MO) calculations, while the orange dotted curves denote the band-additive (BA) Raman responses. The energies of the dominant peak positions are indicated.
• Figure 4: The Raman responses in the $A_{1g}$ (a,d), $B_{1g}$ (b,e), and $B_{2g}$ (c,f) channels for in-plane $d_{x^2 - y^2}$ (a–c) and $d_{xy}$ (d–f) pairing states corresponding to Figs. 2(c) and 2(d). The blue solid curves represent the full multiorbital (MO) calculations, while the orange dotted curves denote the band-additive (BA) Raman responses. The energies of the dominant peak positions are indicated.
• Figure A1: Raman responses in the $A_{1g}$ (a,d), $B_{1g}$ (b,e), and $B_{2g}$ (c,f) channels for the $s_{++}$ (a--c) and $s_{\pm}$ (d--f) pairing states, using the same gap functions as in the main text but at a filling of $n = 1.7$ per site, where the $\gamma$ pocket is absent. The blue solid curves represent the full multiorbital (MO) calculations, while the orange dotted curves denote the band-additive (BA) Raman responses. The energies of the dominant pair-breaking peak positions are indicated.