Discriminating Gap Symmetries of Superconducting La$_3$Ni$_2$O$_7$

Abstract

The discovery of high-T$_c$ superconductor in Ruddlesden-Popper nickelate materials represented by La$_3$Ni$_2$O$_7$ has opened new directions in the quest for unconventional superconductivity. A central unresolved issue concerns the pairing symmetry of the superconducting order. In this paper, we model the superconducting order of La$_3$Ni$_2$O$_7$ using the established Fermi surface structure together with phenomenological pairing functions belonging to $s_\pm$ and $d$-wave symmetry classes, which are the leading possibilities in the current debate. We compute several experimentally accessible observables-including tunneling density of states, point contact spectroscopy, superfluid density, and Raman spectroscopy-each of which exhibits distinct characteristics for different gap symmetries. These quantities provide a concrete and experimentally testable route for identifying the pairing symmetry of La$_3$Ni$_2$O$_7$ and for clarifying the microscopic nature of nickelate superconductivity.

Figures (4)

• Figure 1: Tight-binding dispersion, pairing ansatzes, and tunneling density of states. (a) Tight-binding dispersion along the high symmetry lines in momentum space, with Fermi energy indicated by red dotted line. (b) Two Fermi surfaces obtained from the tight-binding model, where the $\alpha(\beta)$-pocket is highlighted in cyan(pink). (c, d) Two-component pairing function $\Delta_{{\bm{k}}}$ projected along the two Fermi surfaces for the $s_\pm$-wave and $d$-wave pairing states, respectively, with colors corresponding to those in (b). In the case of $s_\pm$, the dashed purple (solid pink) line shows the gapped (nodal) pairing function along the $\beta$-pocket, controlled by the parameter $\delta$. (e, f) Tunneling density of states $\rho(\omega)$ calculated from the pairing function in (c, d), respectively.
• Figure 2: Point contact setup and normalized conductance for nodal $s_\pm$-wave and $d$-wave pairing states. (a, b) Schematic illustration of the point-contact junction for tunneling along the (100) and (110) directions, respectively. The junction consists of two leads aligned along the $x$-direction, and a scattering region (red dashed rectangle) comprising a metallic region on the left (green sites) and La$_3$Ni$_2$O$_7$ on the right (pink sites). The interface contains an interfacial hopping $t_{int}$ and an onsite barrier potential $Z$ on the metallic side of the boundary, as defined in eq. \ref{['eq:Hint']}. (c-f) Normalized point-contact conductance $\sigma(V)$ calculated using KWANT. The pairing symmetry and tunneling directions are: nodal $s_\pm$ along the (100) (c) and (110) (d) , $d$-wave along the (100) (e) and (110) (f). The tunneling direction is indicated by red arrows on the insets.
• Figure 3: Superfluid density calculated for nodal $s_\pm$-wave and $d$-wave pairing ansatzes. (a) Decay in superfluid density $n_S(0)-n_S(T)$ for nodal $s_\pm$-wave, showing a $a(T/\eta_s)^{1/2}$ behavior, as fitted by the dashed line with $a\approx1.14$. (b) $n_S(0)-n_S(T)$ obtained with $d$-wave ansatz, showing a linear in $bT/\eta_d$ decay, as fitting by the red dashed line with $b\approx8.93$. Parameter: $\eta_s=\eta_d=\eta=0.04$eV.
• Figure 4: Raman spectra of nodal $s_\pm$-wave and $d$-wave pairing in $A_{1g}$, $B_{1g}$, and $B_{2g}$ channels. (a) The diagram illustrating the detection of SC gaps at different positions in the BZ in $A_{1g}$, $B_{1g}$, and $B_{2g}$ channels, respectively. The blue areas approximately represent the regions that can be detected. The white line is the Fermi surface. (b) The Raman spectra obtained from three different symmetry types of light fields when the symmetry of the SC gap is nodal $s_{\pm}$-wave. (c) The Raman spectra obtained from three different symmetry types of light fields when the symmetry of the SC gap is $d$-wave. The gray dashed line represents the position of the peak. When the SC gap in the detection region is small, the corresponding Raman spectrum peaks shift to the lower energy.