Mirror-Selective Quasiparticle Interference in Bilayer Nickelate Superconductor

The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates has garnered significant attention. In this study, inspired by recent STM experiments on thin films, we investigate the quasiparticle interference (QPI) characteristics of bilayer nickelates in both normal and superconducting states to identify their Fermiology and pairing symmetry. We demonstrate that the mirror symmetry inherent in the bilayer structure induces mirror-selective quasiparticle scattering by establishing selection rules based on the mirror properties of impurities and the mirror eigenvalues of electronic wavefunctions. This mirror-selective scattering allows for the differentiation of distinct Fermiologies, as QPI patterns vary markedly between scenarios with and without the $d_{z^2}$-bonding Fermi surface (FS). Furthermore, it enables the separate detection of sign changes in superconducting gaps both within the same FS and between different FSs. Crucially, if the mirror-symmetry-enforced selection rules are ignored, the QPI response of an $s_\pm$-wave state can masquerade as that of a conventional $s$-wave state, leading to a misidentification of the pairing symmetry. When combined with field-dependent and reference QPI measurements, this approach facilitates the precise determination of pairing symmetry, even in the presence of FS-dependent gaps and gap anisotropy. Additionally, we discuss practical considerations for STM measurements to effectively identify the pairing symmetry. Our findings demonstrate that mirror-selective QPI is a powerful tool for distinguishing between different Fermiologies and pairing states, which is helpful in pinning down pairing symmetry and revealing the pairing mechanism in bilayer nickelates.

💡 Research Summary

The paper investigates quasiparticle interference (QPI) in bilayer nickelate superconductors, focusing on how the intrinsic mirror symmetry of the two‑NiO₂‑layer structure imposes strict selection rules on impurity scattering. Starting from a realistic two‑orbital (dₓ²₋y² and d_z²) tight‑binding model, the authors generate two distinct Fermi surface (FS) topologies by tuning the chemical potential: (i) a “no‑γ” case where the d_z² bonding band lies below the Fermi level, yielding only α (bonding) and β (antibonding) pockets, and (ii) a “γ‑present” case where the bonding d_z² band crosses the Fermi level, adding a γ pocket around the Brillouin‑zone corner. Because the mirror operator M_z = ℓ_x σ_0 exchanges the top and bottom layers, each FS acquires a definite mirror eigenvalue (+1 for bonding, –1 for antibonding). Consequently, α and γ are mirror‑even, while β is mirror‑odd.

Three representative impurity potentials are introduced: (V₁) a non‑magnetic, intra‑layer, mirror‑even scatterer; (V₂) a non‑magnetic, intra‑layer, mirror‑odd scatterer; and (V₃) an inter‑layer, orbital‑selective (primarily d_z²), mirror‑even scatterer. Within the T‑matrix formalism (Born approximation for clarity), the authors derive analytic selection rules: mirror‑even impurities only connect states with the same mirror eigenvalue (BFS↔BFS or ABFS↔ABFS), while mirror‑odd impurities connect only opposite‑eigenvalue states (BFS↔ABFS). These rules manifest directly in the Fourier‑transformed LDOS: for V₁ and V₃ the QPI intensity shows peaks at q‑vectors linking α↔α, β↔β, or γ↔γ, but no intensity for α↔β or β↔γ. For V₂ the situation is reversed; the usual QPI pattern is essentially absent unless a layer‑resolved LDOS is examined, in which case α↔β and β↔γ scattering appear. The presence of the γ pocket dramatically enhances certain q‑vectors because of its large density of states, providing a clear experimental fingerprint for the debated d_z² bonding FS.

The study then turns to the superconducting state, where the coherence factors introduce an additional “sign‑change” selection rule governed by time‑reversal symmetry. Three pairing symmetries are considered: conventional s‑wave (no sign change), s±‑wave (sign reversal between different FSs), and dₓ²₋y²‑wave (sign change within a single FS and nodes along the Brillouin‑zone diagonals). By evaluating QPI at energies ω = Δ₀ (the gap magnitude) and ω = Δ₀/2, the authors show that mirror‑even impurities (V₁, V₃) produce enhanced intensity at inter‑FS q‑vectors only for the s± state, because the product of gap signs changes sign across those vectors. In contrast, the conventional s‑wave yields no such enhancement, and the d‑wave produces strong intensity along diagonal q‑vectors when probed with the mirror‑odd impurity V₂, reflecting the nodal structure. Thus, a combination of impurity type, energy, and magnetic field (which can break time‑reversal symmetry and modify the coherence factors) enables unambiguous discrimination among the three pairing candidates.

A crucial warning emerges: if the mirror‑selection rules are ignored and QPI is interpreted with the standard “sign‑change” analysis alone, the s± state can masquerade as a plain s‑wave, leading to a misidentification of the pairing symmetry. The authors therefore propose a practical STM protocol: (1) deliberately introduce both mirror‑even and mirror‑odd scatterers (e.g., by adsorbing non‑magnetic atoms on the surface for V₁/V₃ and using a spin‑polarized tip for V₂); (2) acquire field‑dependent FT‑QPI maps to test the robustness of the sign‑change signatures; (3) compare the QPI patterns with and without the γ pocket (which can be tuned by strain or pressure) to confirm the underlying Fermiology.

In summary, the paper establishes “mirror‑selective QPI” as a powerful, symmetry‑driven diagnostic tool. It simultaneously resolves two central controversies in bilayer nickelates: (i) whether the d_z² bonding band contributes to the Fermi surface, and (ii) what the superconducting order‑parameter symmetry is. By exploiting the intrinsic mirror symmetry of the bilayer, the method provides clear, experimentally accessible criteria that go beyond conventional QPI analyses, offering a pathway to pinpoint the pairing mechanism in this emerging high‑T_c family.