Orbital-selective Mottness Driven by Geometric Frustration of Interorbital Hybridization in Pr4Ni3O10

By combining high-resolution angle-resolved photoemission spectroscopy with theoretical calculations, this study reveals that geometric frustration of interorbital hybridization in Pr4Ni3O10 drives an orbital-selective Mott phase characterized by incoherent flat $d_{z^2}$ bands and coherent dispersive $d_{x^2-y^2}$ bands, offering a structural control parameter for understanding correlated states and superconductivity in trilayer nickelates.

The Gist

Imagine a microscopic city built from layers of atoms, where electrons are the citizens trying to move around. In some materials, these electrons flow freely like a busy highway. In others, they get stuck in traffic jams, creating a "Mott" state where they are localized and immobile. This paper explores a special family of materials called nickelates (specifically trilayer nickelates) to understand how to control this traffic.

The researchers compared two very similar cities: one made with Lanthanum (La) and one made with Praseodymium (Pr). While they look almost identical on the map, the behavior of their electron citizens is surprisingly different.

Here is the breakdown of their findings using simple analogies:

1. The Two Types of Electron "Highways"

Inside these materials, electrons live in different "neighborhoods" called orbitals. The study focused on two main types:

• The $d_{x^2-y^2}$ Orbitals: Think of these as the main expressways. They are wide, fast, and the electrons move through them smoothly (coherently).
• The $d_{z^2}$ Orbitals: Think of these as flat, dead-end cul-de-sacs. In the Lanthanum city, these are still connected to the main roads, allowing some traffic to flow.

2. The "Geometric" Twist

The key difference between the two cities is the angle of the bridges connecting the layers.

• In the Lanthanum city: The bridges are slightly more open (a wider angle). This allows the "cul-de-sac" electrons ($d_{z^2}$) to mix well with the "expressway" electrons ($d_{x^2-y^2}$). The result? A healthy, connected flow where both types of electrons work together.
• In the Praseodymium city: The bridges are bent more sharply (a tighter angle). This geometric twist acts like a traffic jam specifically for the cul-de-sac electrons. Suddenly, the $d_{z^2}$ electrons lose their ability to move; they become "incoherent" (confused and stuck) and disappear from the map. However, the main expressways ($d_{x^2-y^2}$) keep running just fine.

The researchers call this an "Orbital-Selective Mott" phase. It's like a city where the side streets are completely gridlocked, but the main highway is still open. This happens because the sharp angle of the Praseodymium structure frustrates the connection between the two types of electron neighborhoods.

3. The "Kondo" Distraction

There is a second factor in the Praseodymium city. The Praseodymium atoms have their own little magnetic "spins" (like tiny, restless magnets).

• In the Lanthanum city, the electrons move in a relatively orderly fashion.
• In the Praseodymium city, these restless magnetic atoms act like distracting street performers or Kondo-like scattering centers. They bump into the electrons, creating extra chaos. This extra noise helps push the already-stuck cul-de-sac electrons into an even deeper state of incoherence.

4. The "Gap" in the Road

Both cities experience a phenomenon called a "density-wave transition," which is like a seasonal road closure that happens at a specific temperature.

• Lanthanum: The road closure (the "gap") is wide and strong (about 12 meV).
• Praseodymium: Even though the road closure happens at a higher temperature (meaning the instability is stronger), the actual size of the gap is smaller (only about 6 meV).

Why? The researchers suggest that the "distracting street performers" (the Praseodymium magnetic moments) are so chaotic that they disrupt the formation of a large, solid gap, even though the conditions for the closure are met.

The Big Picture

The paper concludes that by simply changing the angle of the atomic bridges (the geometry), scientists can toggle between a state where electrons mix freely and a state where they are selectively stuck.

This discovery is crucial because it provides a "control knob" for understanding how these materials behave. Since these nickelates are known to become superconductors (conducting electricity with zero resistance) under high pressure, understanding how to manipulate this "selective stuckness" helps scientists figure out how to engineer better superconductors in the future. The study highlights that the complex dance between the shape of the crystal, the magnetic moments, and electron interactions is what creates these fascinating quantum states.

Technical Summary

Technical Summary: Orbital-Selective Mottness Driven by Geometric Frustration in Pr$_4$Ni$_3$O$_{10}$

Problem Statement
Layered Ruddlesden-Popper (R-P) phase nickelates have emerged as a critical platform for investigating correlated superconductivity in 3d transition metal oxides. While bilayer nickelates offer insights into superconductivity, they often suffer from structural complexity and imperfections. Trilayer nickelates, specifically La$_4$Ni$_3$O$_{10}$ and the recently discovered superconductor Pr$_4$Ni$_3$O$_{10}$ (which exhibits an onset $T_c \approx 40$ K under pressure), offer a more pristine system for studying electronic structures and competing density-wave orders. A central challenge remains in understanding how rare-earth substitution (La vs. Pr) tunes the physical properties. The Pr$^{3+}$ cation introduces dual effects: chemical pressure due to its smaller ionic radius and Kondo-like scattering due to its local magnetic moments. The specific impact of these factors on orbital-selective correlations, Hund's coupling, and interorbital hybridization in the normal state is experimentally elusive, yet crucial for deciphering the mechanism behind the enhanced superconductivity in Pr$_4$Ni$_3$O$_{10}$.

Methodology
The study employs a combined approach of high-resolution angle-resolved photoemission spectroscopy (ARPES) and theoretical calculations.

• Experimental: High-resolution ARPES was performed on single crystals of Pr$_4$Ni$_3$O$_{10}$ and La$_4$Ni$_3$O$_{10}$ using various photon energies (including laser-ARPES at 7 eV and synchrotron radiation up to 160 eV) to map Fermi surfaces and band dispersions. Transport measurements (resistivity) and magnetic susceptibility measurements were conducted to characterize phase transitions and magnetic behavior.
• Theoretical: Density-functional theory (DFT) combined with dynamical mean-field theory (DMFT) calculations were utilized to model the spectral functions. The calculations incorporated on-site Coulomb interaction ($U = 5$ eV) and Hund's coupling ($J_H = 0.8$ eV). Crucially, the authors performed layer-selective calculations and a hypothetical structural substitution (replacing Pr with La while maintaining Pr$_4$Ni$_3$O$_{10}$ structural parameters) to isolate the effects of geometry versus chemical composition.

Key Contributions and Results

1. Orbital-Selective Mottness: The study reveals a striking dichotomy in the electronic coherence between the two compounds. In La$_4$Ni$_3$O$_{10}$, the system exhibits pronounced interorbital hybridization where the flat $d_{z^2}$ band (located ~30 meV below $E_F$) and the dispersive $d_{x^2-y^2}$ bands are both coherent. In contrast, Pr$_4$Ni$_3$O$_{10}$ displays an orbital-selective Mott (OSM) phase: the flat $d_{z^2}$ band becomes markedly incoherent with depleted spectral weight, while the dispersive $d_{x^2-y^2}$ bands retain their coherence.
2. Geometric Control via Bonding Angle: DFT+DMFT calculations identify the interlayer Ni-O-Ni bonding angle as the primary control parameter. The smaller ionic radius of Pr reduces this angle from 165$^\circ$ (La) to 158$^\circ$ (Pr). The calculations demonstrate that this geometric distortion, rather than the chemical identity of the rare earth alone, drives the $d_{z^2}$ orbitals into an incoherent state. This geometric frustration suppresses interorbital hybridization, effectively localizing the $d_{z^2}$ electrons.
3. Impact on $d_{x^2-y^2}$ Correlations: The incoherence of the $d_{z^2}$ band in Pr$_4$Ni$_3$O$_{10}$ frustrates the interorbital hybridization that typically delocalizes electrons. Consequently, the screening provided by $d_{z^2}$ electrons is reduced, leading to an enhanced correlation effect (renormalization) in the $d_{x^2-y^2}$ bands, evidenced by a "waterfall"-like dispersion anomaly at lower energies compared to La$_4$Ni$_3$O$_{10}$.
4. Density-Wave Transition Anomalies: Both compounds exhibit charge/spin-density-wave transitions ($T_{dw} \approx 156$ K for Pr, 135 K for La). However, despite the higher $T_{dw}$ in Pr$_4$Ni$_3$O$_{10}$, the density-wave gap is significantly reduced ($\Delta_0 \approx 6$ meV) compared to La$_4$Ni$_3$O$_{10}$ ($\Delta_0 \approx 12$ meV). The authors attribute this reduction to the local magnetic moments of Pr$^{3+}$ cations, which act as Kondo-like scattering centers and create additional spin fluctuation channels that disrupt the phase stiffness of the long-range density-wave order.

Significance
The paper establishes that the interplay among lattice geometry, orbital degrees of freedom, and spin fluctuations creates a tunable landscape for correlated states in trilayer nickelates. By identifying the interlayer Ni-O-Ni bonding angle as a structural parameter that modulates the orbital-selective Mott phase, the work provides a concrete framework for understanding the emergence of superconductivity under high pressure. The findings highlight a similarity between the multi-orbital physics in nickelates and iron-based superconductors, suggesting that the competition between orbital-selective correlations and interorbital hybridization is a fundamental mechanism governing the normal-state density-wave orders and the subsequent superconducting phase. The results imply that Pr$_4$Ni$_3$O$_{10}$ may host a quantum critical point between the OSM phase and pressurized superconductivity, tunable via structural parameters.