Multimodal Terahertz Spectroscopy of the Pairing Symmetry and Normal-State Pseudogap in (La,Pr)$_3$Ni$_2$O$_7$ Films

Abstract

The discovery of ambient-pressure superconductivity in compressively strained (La,Pr)$_3$Ni$_2$O$_7$ thin films has intensified efforts to identify the pairing mechanism. However, the symmetry of the superconducting order parameter and the character of the normal state remain unsettled. Here we combine bulk-sensitive terahertz (THz) time-domain spectroscopy with THz third-harmonic generation to present spectroscopic insights into these issues. Linear THz spectroscopy reveals a bulk superconducting response in the (La,Pr)$_3$Ni$_2$O$_7$ films, evidenced by the suppression of low-frequency spectral weight below the onset critical temperature, $T_\mathrm{c}^{\mathrm{onset}}$. A weak coherence peak near $T_\mathrm{c}^{\mathrm{onset}}$, together with substantial residual low-frequency conductivity as $T\to 0$, is consistent with disordered $s_{\pm}$-wave pairing. In the nonlinear regime, the third-harmonic signal rises sharply on cooling through $T_\mathrm{c}^{\mathrm{onset}}$, providing an independent signature of the transition. Strikingly, the nonlinear response persists above $T_\mathrm{c}^{\mathrm{onset}}$, pointing to either disorder-enhanced nonlinearity or a distinct correlated normal state. Motivated by angle-resolved photoemission spectroscopy on similarly grown films that identifies a comparable temperature scale, we associate the anomalous normal-state terahertz nonlinearity with a pseudogap. These results establish (La,Pr)$_3$Ni$_2$O$_7$ as a bulk superconductor with $s_{\pm}$-like pairing that coexists with, and may compete with, a distinct ordered state, providing a platform for exploring unconventional superconductivity beyond cuprates and pnictides.