Electronic theory for scanning tunneling microscopy spectra in bilayer nickelate thin films

arXiv:2606.31569 · cond-mat.supr-con, cond-mat.str-el · Submitted 2026-06-30 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Electronic theory for scanning tunneling microscopy spectra in bilayer nickelate thin films".

Mira: Recent Scanning Tunneling Microscopy (STM) experiments measuring superconducting gap features in thin films of bilayer nickelates have paved the way to study Cooper-pairing models and band-selective identification of gap features…

Kai: First, who's behind it and why it matters.

Paper summary: Kai: We've been looking at how this paper uses electronic theory to tackle the mysteries of superconducting gap features in bilayer nickelates, focusing on La2PrNi2O7 at ambient pressure and compressive strain <ref:2606.31569#pg0>. The core thesis is that by employing a realistic two-orbital model and the continuum Green's function formalism, they can theoretically analyze orbital and band-selective local density of states as well as the corresponding STM spectra <ref:2606.31569#pg0>.

Mira: What this means in practice is that they demonstrate that the multiorbital character and how the Wannier functions depend on where you place your scanning tunneling microscope tip leads to STM spectra with characteristic features depending on that position <ref:2606.31569#pg0>. This enables a band-resolved analysis of superconducting coherence peaks and scattering momenta, which is what makes the work so relevant <ref:2606.31569#pg0>.

Lev: So, they are claiming that this theoretical framework can predict spectral signatures that are position-dependent in a way that matches experimental observations from STM experiments <ref:2606.31569#pg0>. That's a big step toward connecting the fundamental physics of the pairing to what we actually measure with an STM probe.

Kai: Right, and they go further by showing that tip height-dependent measurements can clearly distinguish between the coherence peaks’ band origin and the actual symmetry of the superconducting order parameter <ref:2606.31569#pg1>. This is a direct way to test their models against experimental data.

Mira: Furthermore, they study the response of isolated impurities by substituting a Ni atom or an apical oxygen atom between layers using the T-matrix approach <ref:2606.31569#pg1>. The result shows that quasiparticle interference patterns measured in STM can unambiguously distinguish between candidate superconducting structures <ref:2606.31569#pg1>.

Lev: That's significant because it moves beyond just looking at the clean system to how the system reacts when perturbed, which is often where real experimental noise and complexity come into play <ref:2606.31569#pg1>.

Kai: And they even show how using an antisymmetrized HAEM prescription allows them to robustly detect the sign change of the superconducting order parameter by comparing s plus or minus and s++ gaps <ref:2606.31569#pg1>. This is a powerful tool for probing the underlying pairing mechanism.

Mira: Overall, the paper establishes a unified framework that links impurity symmetry, gap structure, and STM observables in bilayer nickelates <ref:2606.31569#pg0>. It provides concrete guidance for future STM investigations by offering criteria to determine the incipient nature of the gamma-band and distinguish between competing superconducting gap symmetries <ref:2606.31569#pg0>.

Lev: If they provide those criteria, it means we can start designing experiments with a much clearer target based on this paper's theoretical predictions <ref:2606.31569#pg0>.

Kai: It really boils down to using Wannier-resolved continuum modeling and channel-selective QPI analysis to guide future STM investigations in these complex systems <ref:2606.31569#pg0>. This sets a new standard for how we interpret these spectral maps.

Conclusion: Kai: So, looking at the title "Electronic theory for scanning tunneling microscopy spectra in bilayer nickelate thin films," it really highlights how deeply this work connects fundamental electronic structure theory with experimental observation from STM <ref:2606.31569#pg0>. The authors, Scholten, B¨otzel, Lechermann, Choubey, and Eremin, have built a model that's powerful because it incorporates the realistic two-orbital bilayer model derived from first principles calculations <ref:2606.31569#pg1>.

Mira: The implications of this work are substantial because it gives us a concrete theoretical roadmap for understanding how to interpret the data we collect in these experiments <ref:2606.31569#pg0>. It moves beyond just observing spectra to providing the tools to predict what those spectra should look like based on different pairing symmetries and tip positions <ref:2606.31569#pg1>.

Lev: For researchers working on quantum error correction, having a more robust way to characterize these pairing structures through STM could inform how we approach realizing superconducting states in any platform, even if it's not exactly the nickelates studied here <ref:2606.31569#pg0>.

Kai: In simpler terms, this paper tells us that we can use a combination of Wannier-resolved continuum modeling and channel-selective QPI analysis to get experimentally accessible criteria for figuring out the incipient nature of the gamma-band and sorting out which superconducting gap symmetry is dominant <ref:2606.31569#pg0>.

Mira: This approach offers concrete guidance for future STM investigations, essentially giving experimentalists a way to use these sophisticated theoretical tools to make informed decisions about what to look for next <ref:2606.31569#pg0>.

Lev: If this framework holds up when applied to real hardware measurements, it means we have a solid theoretical foundation for interpreting the complex physics of correlated electron systems in thin films <ref:2606.31569#pg0>.

Kai: It really establishes a new way of thinking about how we use STM data—not just as a collection of peaks, but as detailed spatial maps that reveal the underlying orbital and symmetry information <ref:2606.31569#pg0>.

Theoretische Physik III, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum · Department of Physics, Indian Institute of Technology Roorkee

cond-mat.supr-con, cond-mat.str-el

Submitted: 2026-06-30

Updated: 2026-06-30

DOI: 10.1103/68r6-8v6v

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 81/100

The gist: Recent Scanning Tunneling Microscopy (STM) experiments measuring superconducting gap features in thin films of bilayer nickelates have paved the way to study Cooper-pairing models and band-selective

Key concepts

Wannier Orbital Projection
This technique transforms complex DFT band structures into localized orbitals that better describe electronic states in real space. It helps define how electrons are spatially localized within the nickelate layers, which is crucial for understanding how STM tip position affects the measured spectral features.
Continuum Green’s Function Approach
This method uses a mathematical framework to calculate the local density of states (LDOS) at any point, including where the STM tip is located. Unlike simple lattice calculations, this approach accurately captures the local symmetry relevant to the tip's position.
Quasiparticle Interference (QPI)
QPI patterns are signatures observed in STM experiments when an impurity perturbs the superconducting state. Analyzing these patterns allows researchers to unambiguously distinguish between different candidate superconducting structures, such as s± and d-wave pairing, by looking at the resulting electronic scattering features.

Terminology

Summary

Recent Scanning Tunneling Microscopy (STM) experiments measuring superconducting gap features in thin films of bilayer nickelates have paved the way to study Cooper-pairing models and band-selective identification of gap features in these systems.

The gist: The multiorbital character and the spatial dependence of the Wannier functions lead to STM spectra developing characteristic features depending on the position of the scanning tunneling microscope’s tip, allowing for a band-resolved analysis of superconducting coherence peaks and scattering momenta.

Model Construction

The starting point to model the bilayer system is a non-interacting Hamiltonian defined by Eq. (1), which describes electrons in layer l and Ni-3d orbital µ with momentum k = (kx, ky). The matrix elements of this tight-binding Hamiltonian are described by the maximally localized Wannier orbital projection of the DFT band structure on the 3dx2−y2 - and 3dz2-orbitals in each layer, including slave-boson renormalization. This results in a two-orbital bilayer Hamiltonian, Hˆ0(k), which is block-diagonalized into bonding and antibonding bands using the transformation c b/a kσ,µ = √1/2 (ckσ,1µ ± ckσ,2µ).

Superconducting State Formulation

The superconducting state is included straightforwardly on a mean-field level by expanding the bilayer basis to the Bogoliubov-Nambu space. This leads to the Cooper-pairing Hamiltonian Hpair (Eq. 3), which includes the gap function Dˆ(k) defined in Eq. (4). The main superconducting instabilities vary between dx2−y2 - (or dxy) wave and bonding-antibonding s±-wave symmetries, with the latter seeming to dominate in most scenarios, although results may depend sensitively on the relative strength of intra- versus interlayer antiferromagnetic spin fluctuations.

Local Density of States and Tip Position

To compare theoretical calculations with experimental STM measurements, a continuum Green’s function approach is employed using Eq. (6) for the continuum Green’s function Gˆ(r, r′, ω). This method allows for the definition of the continuum LDOS at the STM tip position r as ρ(r, ω) = −2π Im n Gˆ11(r, r, ω) (Eq. 7). Unlike lattice-based calculations that yield LDOS at lattice sites only, this approach correctly captures the local symmetry at the STM tip position because the wave function of the STM tip couples differently to orbital space matrix.

Distinguishing Gap Symmetries via Tip Height

Tip height-dependent measurements can clearly distinguish between the coherence peaks’ band origin and the actual symmetry of the superconducting order parameter. In an incipient γ-band case, a clear trend emerges: the spectral weight of the α-band coherence peak at 7 meV decreases significantly faster than that of the βband coherence peak at 19 meV with increasing distance z. This suggests that the α-band LDOS is more strongly suppressed with increasing height, which may explain the weak shoulder observed in STM experiments.

Impurity Effects and QPI Signatures

The response of an isolated impurity is studied via the T-matrix approach, leading to quasiparticle interference (QPI) patterns measured in STM experiments. The manuscript demonstrates that QPI patterns can unambiguously distinguish between the candidate superconducting structures. Specifically, for mirror-symmetric apical oxygen impurities (Vˆ3), the QPI signal exhibits features that are almost exclusively of dz2-character, which shadows other contributions in the crossing case, revealing qualitative differences between s± and d-wave pairing. Furthermore, using the antisymmetrized HAEM prescription, it is shown that this method robustly detects the sign change of the superconducting order parameter by comparing s± and s++ gaps.

Conclusion

The work establishes a unified framework linking impurity symmetry, superconducting gap structure, and STM observables in bilayer nickelates. A combination of Wannier-resolved continuum modeling, channel-selective QPI analysis, HAEM antisymmetrization, can provide experimentally accessible criteria to determine the incipient nature of the γ-band and distinguish between competing superconducting gap symmetries. This approach offers concrete guidance for future STM investigations.

Appendix A: Superconducting Gaps

Table I lists intraorbital pairing strength coefficients for different gap symmetries and orbitals, while Table II presents coefficients for a special model that reverses the projected α- and β-band gap values in the incipient γ-band case. Figure A.1 shows the projected gap on the Fermi surface for s±-wave, d-wave, and s++-wave symmetries across both incipient and crossing γ-band scenarios.

**Table I: Intraorbital pairing strength coefficients for the different gap symmetries and orbitals.

Improvements for AI systems

Here are specific improvements to AI systems based on the insights from this scientific paper:

  1. Improve materials science simulation and prediction accuracy for correlated electron systems, especially bilayer nickelates.

  2. Develop machine learning models capable of predicting the superconducting gap symmetry (s± vs d-wave) in complex multiorbital thin films based on STM/ARPES data signatures.

  3. Enhance quantum chemistry and condensed matter physics simulations by incorporating continuum Green's function formalisms with realistic Wannier functions for accurate local density of states (LDOS) mapping at arbitrary tip positions.

  4. Create tools for orbital-selective electronic structure analysis, allowing AI to distinguish between contributions from different atomic orbitals (e.g., 3dx2-y2 vs 3dz2) in bilayer systems by analyzing their distinct spatial decay and momentum-space distributions.

  5. Implement advanced spectral analysis techniques for experimental data (like QPI patterns) that can robustly disentangle competing superconducting gap symmetries by exploiting channel-selective scattering features (e.g., distinguishing between bb, aa, and ba channels based on impurity placement).

  6. Build AI systems capable of predicting the effect of structural perturbations (like apical oxygen impurities) on superconducting signatures in thin films by modeling how these impurities selectively enhance or suppress specific interband scattering channels.

  7. Create phase-sensitive analysis tools for spectroscopic data that can robustly detect the sign change of the superconducting order parameter (e.g., distinguishing s± from s++ gaps) using advanced techniques like the HAEM prescription applied to momentum-integrated QPI signals.

These improved AI systems will be able to:

  1. Accurately predict and classify novel superconducting phases in complex, multiorbital materials before costly experiments are conducted.

  2. Provide quantitative, spatially resolved maps of electronic properties (LDOS) directly relevant to STM tip locations, overcoming the limitations of lattice-based models.

  3. Identify the dominant pairing symmetry (s± vs d-wave) in experimental data by analyzing subtle, distance-dependent spectral weight changes and QPI features that are currently difficult for human experts to separate reliably.

  4. Determine if a material exhibits an incipient superconducting phase (like the γ-band) by identifying specific, characteristic spectral signatures (e.g., the unique scattering vector patterns associated with its orbital character).

  5. Design targeted experimental strategies by predicting which impurity placement (layer site vs. apical oxygen) will yield the clearest signature for distinguishing between competing pairing symmetries.

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