Prediction of several Co-based La$_3$Ni$_2$O$_7$-like superconducting materials

This paper predicts that electron-doped Co-based analogs of the high-pressure bilayer nickelate La$_3$Ni$_2$O$_7$, specifically LaTh$_2$Co$_2$O$_7$, La$_3$Ni$_2$O$_5$Cl$_2$, and La$_3$Ni$_2$O$_5$Br$_2$, exhibit strongly correlated electronic states with $s$-wave superconductivity as the leading pairing symmetry.

The Gist

Imagine the world of superconductors (materials that conduct electricity with zero resistance) as a high-stakes cooking competition. For decades, chefs (scientists) have been trying to perfect a specific "recipe" for high-temperature superconductivity.

So far, they've found success with ingredients based on Copper (the classic dish), Iron (a popular modern twist), and Nickel (a brand-new, exciting flavor discovered recently). But there's one major ingredient that has stubbornly refused to work: Cobalt.

This paper is like a brilliant food critic and theoretical chef saying, "Wait a minute! If Nickel works so well, and Cobalt is its next-door neighbor in the periodic table (like two siblings who look very similar), maybe we just haven't cooked the Cobalt dish correctly yet."

Here is the breakdown of their discovery in simple terms:

1. The Inspiration: The "Nickel Miracle"

Recently, scientists discovered that a specific Nickel-based material called La₃Ni₂O₇ becomes a superconductor at surprisingly high temperatures (around 80 Kelvin, or -193°C) when you squeeze it with immense pressure.

• The Secret Sauce: This material has a unique "double-layer" structure (like a sandwich). Inside, the electrons are dancing in a very specific, chaotic, yet coordinated way. They are "strongly correlated," meaning they don't move independently; they react to each other like a crowded dance floor where everyone is holding hands.

2. The Problem: The Missing Cobalt

Cobalt is chemically very similar to Nickel. In fact, they are right next to each other on the periodic table. Scientists have tried to make Cobalt superconductors before, but they only got them to work at extremely low temperatures (near absolute zero), which isn't very useful. The big question was: Can we make Cobalt behave like that "miracle" Nickel?

3. The Solution: The "Twin Swap" Recipe

The authors of this paper used powerful computer simulations to design a new recipe. They took the high-pressure Nickel structure and asked, "What if we swapped the Nickel atoms for Cobalt atoms?"

But there was a catch. Cobalt has a different number of electrons than Nickel. If you just swap them, the "dance floor" gets unbalanced, and the magic stops.

• The Fix: They realized they needed to add a little bit of "electron seasoning." They proposed doping the material (adding extra electrons) by swapping some atoms for others (like swapping a neutral atom for a slightly negative one).
• The Result: They predicted three new "Cobalt Twins":
  1. LaTh₂Co₂O₇ (Swapping in Thorium)
  2. La₃Co₂O₅Cl₂ (Swapping in Chlorine)
  3. La₃Co₂O₅Br₂ (Swapping in Bromine)

4. Why It Might Work: The "Perfect Crowd"

The paper explains that for superconductivity to happen, the electrons need to be in a "Goldilocks zone"—not too calm, not too chaotic, but just right.

• The Magnetism Check: In the Nickel material, the atoms have a specific magnetic "spin" (like tiny compass needles). The researchers found that in their new Cobalt recipes, the magnetic spins are almost identical to the Nickel ones.
• The "Sweet Spot": They calculated that the Cobalt atoms in these new materials fall into a very narrow, perfect window of magnetic behavior that is known to trigger high-temperature superconductivity. It's like tuning a radio to the exact frequency where the music is clearest.

5. The Prediction: S-Wave Dancing

Using mathematical models (Random Phase Approximation), they predicted how these electrons would pair up.

• In many superconductors, electrons pair up in complex, twisted ways.
• In these new Cobalt materials, the electrons seem to pair up in a simple, symmetrical "S-wave" pattern. Think of it like a couple holding hands and spinning in a perfect circle. This is a very stable and promising way to conduct electricity without resistance.

The Bottom Line

This paper is a theoretical map. The authors haven't built these materials in a lab yet. Instead, they have used supercomputers to say: "If you build these specific Cobalt compounds and squeeze them with pressure, you might just discover the next generation of high-temperature superconductors."

Why does this matter?
If they are right, it opens up a whole new family of materials for us to explore. Just as Iron-based superconductors gave us new tools, these Cobalt-based ones could lead to even better technologies, from lossless power grids to ultra-fast quantum computers. It's a call to action for experimental scientists to go into the lab and try to cook up these "Cobalt dishes" to see if they taste as good as the theory predicts.

Technical Summary

1. Problem Statement

High-temperature superconductivity (HTS) has been established in Copper (Cu), Iron (Fe), and Nickel (Ni) based compounds. However, despite Cobalt (Co) being adjacent to Ni in the periodic table and possessing tunable spin states, high-temperature unconventional superconductivity has not yet been realized in Co-based materials.

Previous Co-based superconductors (e.g., $Na_xCoO_2 \cdot H_2O$, $LaCo_2B_2$) exhibit very low critical temperatures ($T_c < 7$ K) and often involve conventional pairing mechanisms or structural complexities that hinder high-$T_c$ exploration. The recent discovery of high-$T_c$ superconductivity ($T_c \approx 80$ K) in pressurized bilayer nickelate $La_3Ni_2O_7$ (LNO) provides a new paradigm. LNO's superconductivity is driven by:

• A bilayer crystal structure.
• Strong interlayer hopping creating bonding/antibonding bands from nearly half-filled $Ni$ $d_{z^2}$ orbitals.
• Strong electronic correlations, specifically Hund's coupling and interlayer antiferromagnetic correlations.

The central question is whether Cobaltates can be engineered to mimic the specific electronic and structural characteristics of LNO to achieve similar high-$T_c$ superconductivity.

2. Methodology

The authors employed a multi-step theoretical approach combining Density Functional Theory (DFT) and Dynamical Mean-Field Theory (DMFT) to investigate candidate materials.

• Material Design:

  • They started with the high-pressure phase of $La_3Co_2O_7$ (LCO), which is isostructural to LNO but has a Co valence of +2.5 ($3d^{6.5}$).
  • To mimic the $3d^{7.5}$ configuration of Ni in LNO, they introduced electron doping via two strategies:
    1. Substituting La with tetravalent Thorium (Th): Resulting in $LaTh_2Co_2O_7$ (LCO-Th).
    2. Substituting O with monovalent Chlorine (Cl) or Bromine (Br): Resulting in $La_3Co_2O_5Cl_2$ (LCO-Cl) and $La_3Co_2O_5Br_2$.
  • These substitutions reduce the Co valence to +1.5, achieving the target $3d^{7.5}$ configuration.

• Computational Techniques:

  • Structural Optimization: DFT was used to optimize crystal structures at high pressure (25 GPa for LCO, 29.5 GPa for LNO) to ensure dynamical stability (verified via phonon spectra).
  • Electronic Structure: DFT+DMFT was used to calculate spectral functions, self-energies, and local magnetic moments, accounting for strong electron correlations.
  • Model Construction: Tight-binding (TB) models were fitted to the DFT bands to isolate the $e_g$ orbitals ($d_{z^2}$ and $d_{x^2-y^2}$).
  • Pairing Symmetry: The Random Phase Approximation (RPA) was applied to the TB models to determine the leading superconducting pairing symmetry and gap structure.

3. Key Contributions

1. Identification of New Candidates: Theoretically identified $LaTh_2Co_2O_7$, $La_3Co_2O_5Cl_2$, and $La_3Co_2O_5Br_2$ as promising Co-based analogs to the superconducting LNO.
2. Validation of Electronic Similarity: Demonstrated that these doped cobaltates possess electronic structures (bandwidths, orbital occupancies) and correlation strengths remarkably similar to LNO.
3. Prediction of Pairing Symmetry: Predicted that s-wave (specifically $s$-wave or $s_{\pm}$-wave) is the leading pairing symmetry in these Co-based systems, driven by strong interlayer correlations.
4. Magnetic Moment Alignment: Showed that the calculated local magnetic moments of Co in these compounds fall precisely within the "optimal window" ($\approx 0.63–0.68 \mu_B$) recently identified as critical for high-$T_c$ in nickelates.

4. Key Results

A. Structural and Electronic Similarity

• Crystal Structure: The optimized structures of LCO-Th and LCO-Cl at high pressure are dynamically stable and closely resemble LNO, with comparable bond lengths and angles.
• Band Structure: The $Co$ $e_g$ bands in the doped compounds span a similar energy range to Ni in LNO ($\sim 3.8$ eV bandwidth).
• Self-Doping Effect: In LCO-Th, Th $4f$ bands cross the Fermi level, and in LCO-Cl, La $5d$ bands appear near the Fermi level. This mimics the "self-doping" effect seen in infinite-layer nickelates, which does not suppress superconductivity.
• Correlation Strength: DFT+DMFT calculations show that the $e_g$ bands become significantly broadened and renormalized, forming nearly flat bands at the Fermi level, indicating strong correlations comparable to LNO.

B. Correlation and Magnetic Properties

• Self-Energy ($\Sigma$): The imaginary part of the self-energy, $Im\Sigma(i\omega_n)$, for the $Co$ $d_{z^2}$ orbital in doped LCO exhibits a profile nearly identical to the $Ni$ $d_{z^2}$ in LNO, signaling non-Fermi liquid or strange metal behavior.
• Orbital Occupancy: The $Co$ $d_{z^2}$ orbitals are nearly half-filled ($N_d \approx 1.0$), similar to Ni in LNO, which is crucial for strong correlations. The $d_{x^2-y^2}$ orbitals have an occupancy of $\sim 0.73$, sufficient to sustain Hund's coupling.
• Local Magnetic Moments: The calculated local magnetic moments for Co in these compounds range from 0.637 to 0.647. This aligns perfectly with the narrow window ($0.63–0.68$) identified in previous studies as optimal for high-$T_c$ superconductivity in Ruddlesden-Popper nickelates.

C. Superconducting Instability

• Fermi Surfaces: The constructed TB models reveal Fermi surfaces with multiple sheets (e.g., $\alpha, \beta, \gamma$ for LCO-Th).
• Pairing Symmetry: RPA calculations indicate that the leading pairing instability is s-wave.
  • For LCO-Th: The gap function belongs to the $A_{1g}$ irreducible representation (s-wave).
  • For LCO-Cl: The leading pairing is $s_{\pm}$-wave.
• Critical Interaction: The critical interaction strength ($U_c$) required to drive the spin susceptibility divergence is found to be $\sim 1.0$ eV, suggesting that realistic interaction strengths in these materials are sufficient to induce superconductivity.

5. Significance and Outlook

• Bridging the Gap: This work provides a theoretical blueprint for discovering high-temperature superconductivity in Cobalt-based systems, a field that has lagged behind Cu, Fe, and Ni systems.
• Design Strategy: It validates a design strategy based on structural analogy (bilayer Ruddlesden-Popper), electron doping to tune valence, and theoretical modeling of multi-orbital correlations.
• Experimental Guidance: The paper explicitly calls for the synthesis of these specific compounds ($LaTh_2Co_2O_7$, $La_3Co_2O_5Cl_2$, etc.) under high pressure. It suggests that if synthesized, these materials could host high-$T_c$ superconductivity driven by similar mechanisms to LNO.
• Future Directions: The authors suggest extending this strategy to other rare-earth substitutions, hydrogen doping, and exploring trilayer analogs (like $La_4Ni_3O_{10}$) where Co's natural $3d$ electron count ($3d^6$–$3d^8$) might offer even more favorable conditions for superconductivity than Ni.

In summary, the paper predicts that electron-doped bilayer cobaltates are the missing link in the family of high-$T_c$ superconductors, possessing the necessary electronic correlations and magnetic moments to potentially rival the performance of nickelates.