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Layer-Resolved Impurity States Reveal Competing Pairing Mechanisms in Trilayer Nickelate Superconductor La$_4$Ni$_3$O$_{10}$

Suyin Zheng, Tao Zhou

Abstract

Trilayer Ruddlesden-Popper nickelate superconductor $\mathrm{La}_4 \mathrm{Ni}_3 \mathrm{O}_{10}$ has generated considerable interest due to its unconventional superconductivity and complex electronic structure. Notably, $\mathrm{La}_4 \mathrm{Ni}_3 \mathrm{O}_{10}$ features a mixed Ni valence state and an asymmetric trilayer configuration, leading to distinct quasiparticle distributions and local density of states (LDOS) between the inner and outer NiO$_2$ planes. In this work, we investigate impurity-induced states in $\mathrm{La}_4 \mathrm{Ni}_3 \mathrm{O}_{10}$ using a two-orbital model combined with $T$-matrix formalism, focusing on the contrasting roles of intra- and interlayer pairing channels. Our self-consistent mean-field analysis reveals that interlayer pairing results in partially gapless Fermi surfaces, with unpaired quasiparticles concentrated in the outer layers and a pronounced low-energy LDOS. We demonstrate that impurity effects vary significantly depending on both the pairing symmetry and impurity location: interlayer-dominant pairing produces sharp resonance states when impurities are in the inner layer, whereas impurities in the outer layer lead to in-gap enhancements without sharp resonances; in contrast, intralayer-dominant pairing generally yields increased in-gap LDOS without sharp impurity resonances, regardless of impurity position. These findings suggest that single-impurity spectroscopy can serve as a powerful probe to distinguish between competing superconducting pairing mechanisms in trilayer nickelates and highlight the rich physics arising from their multilayer structure.

Layer-Resolved Impurity States Reveal Competing Pairing Mechanisms in Trilayer Nickelate Superconductor La$_4$Ni$_3$O$_{10}$

Abstract

Trilayer Ruddlesden-Popper nickelate superconductor has generated considerable interest due to its unconventional superconductivity and complex electronic structure. Notably, features a mixed Ni valence state and an asymmetric trilayer configuration, leading to distinct quasiparticle distributions and local density of states (LDOS) between the inner and outer NiO planes. In this work, we investigate impurity-induced states in using a two-orbital model combined with -matrix formalism, focusing on the contrasting roles of intra- and interlayer pairing channels. Our self-consistent mean-field analysis reveals that interlayer pairing results in partially gapless Fermi surfaces, with unpaired quasiparticles concentrated in the outer layers and a pronounced low-energy LDOS. We demonstrate that impurity effects vary significantly depending on both the pairing symmetry and impurity location: interlayer-dominant pairing produces sharp resonance states when impurities are in the inner layer, whereas impurities in the outer layer lead to in-gap enhancements without sharp resonances; in contrast, intralayer-dominant pairing generally yields increased in-gap LDOS without sharp impurity resonances, regardless of impurity position. These findings suggest that single-impurity spectroscopy can serve as a powerful probe to distinguish between competing superconducting pairing mechanisms in trilayer nickelates and highlight the rich physics arising from their multilayer structure.

Paper Structure

This paper contains 7 sections, 23 equations, 9 figures.

Table of Contents

  1. Introduction
  2. MODEL AND FORMALISM
  3. RESULTS AND DISCUSSION
  4. SUMMARY
  5. Impurity effect with different impurity strengths
  6. Layer and orbital resolved zero-energy normal state spectral function
  7. Further analysis of the $T$-matrix denominator

Figures (9)

  • Figure 1: Self-consistent mean-field results for the superconducting order parameters as a function of the intralayer pairing potential, with the interlayer pairing potential fixed at $0.8$.
  • Figure 2: LDOS spectra in the case of dominant interlayer pairing. Solid and dashed lines denote spectra near a point impurity and the bare spectra (without impurity), respectively. Panels (a) and (b) show the LDOS for pure interlayer pairing, with the impurity located on the outer layer and inner layer, respectively. Panels (c) and (d) correspond to the same impurity positions as in (a) and (b), but with an additional, smaller intralayer pairing component included.
  • Figure 3: Similar to Fig. \ref{['fig2']}, but illustrating the scenario in which intralayer pairing dominates.
  • Figure 4: Superconducting gap distribution along the normal-state Fermi surfaces for various pairing interaction parameters $(V_\parallel,V_\perp)$: (a) $(0,0.8)$; (b) $(0.6,0.8)$; (c) $(0.8,0)$; and (d) $(0.8,0.4)$.
  • Figure 5: Real and imaginary parts of the function $D(\omega)$ for pure interlayer pairing (upper panels) and pure intralayer pairing (lower panels). The left and right panels correspond to the outer-layer and inner-layer impurities, respectively.
  • ...and 4 more figures