Superconductivity of bilayer two-orbital Hubbard model for La 3 Ni 2 O 7 under high pressure

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

Kai: We're looking at the paper: "Superconductivity of bilayer two-orbital Hubbard model for La 3 Ni 2 O 7 under high pressure".

Mira: Here's the gist of the paper. The gist The investigation maps a quantum phase diagram of a bilayer two-orbital Hubbard model for La3Ni2O7 under increasing pressure, revealing that superconductivity (SC) is suppressed by pressure and transitions to a Luttinger liquid above 80 GPa Model and Methodology The study employs density functional theory (DFT) combined with density matrix renormalization group (DMRG) calculations to investigate the unusual pressure dependence of the superconducting transition temperature (Tc) in La3Ni2O7 The researchers map a quantum phase diagram of a bilayer two-orbital Hubbard model with increasing pressure in a ladder geometry, which has an intermediate Hubbard repulsion and a Hund’s coupling They use hopping integrals and on-site potentials obtained by fitting the DFT band structures to construct the TB model parameters under different pressures Electronic Structure and Phase Diagram The electronic structure calculations reveal that as pressure increases, the bandwidth of the Ni-eg sector broadens, accompanied by an enlargement of the energy gap between the bonding (γ) and antibonding (γan) bands The TB model yields three pockets on the Fermi surface: a flat hole pocket γ around the M corner mainly characterized by the dz2 orbital, and electron pockets α and β dominated by a mix of dz2 and dx2-y2 orbitals The DMRG calculation on a ladder geometry, considering an intermediate Hubbard repulsion (U = 4.0 eV) and Hund’s coupling (JH = 0.5 eV), maps the quantum phase diagram with increasing pressure Competing Orders The phase diagram shows that for electron filling ηe = 3/8 − 11/32, a density wave phase with a strong spin density wave (SDW) order in both dz2 and dx2-y2 orbitals exists without a static charge density wave (CDW) At 3/8 filling, the SDW exhibits a spin configuration similar to the spin-charge stripe order along a lattice direction At lower filling, ηe = 21/64, a superconducting phase emerges with interlayer SC in both orbitals and in-plane SC in the dz2 orbital, accompanied by suppression of the SDW Pressure Dependence of Superconductivity The superconducting phase is weakened with increasing pressure and transits to a Luttinger liquid (LL) above 80 GPa, which qualitatively agrees with the experimental observation of decreasing Tc in La3Ni2O7 By examining the variation of model parameters, a moderate decrease in the ratio of interaction to hopping integral is shown to make an important contribution for the weakening of SC In Fig.

Kai: 5(b), experimental data show that from 20 GPa to 80 GPa, the transition temperature of SC decreases monotonically, and the SC gives way to a Fermi liquid above 80 GPa Pairing Symmetry and Correlation Functions For ηe = 21/64, interlayer SC in both orbitals is found with power exponents KzSC ≈ 1 and KxSC ≈ 1.5 at 21.6 GPa With increasing pressure, the interlayer SC in both orbitals are gradually weakened, characterized by the increase of power exponents KµSC The disappearance of SC above 80 GPa is characterized by an increase in KzSC and a transition to LL driven by increased pressure The ratio of interaction to hopping integral is found to be a primary ingredient for the weakening of SC Magnetic Order Interplay In the SDW phase, magnetic moments in both orbitals show very slow power-law decay from the boundary to the bulk, characterizing a strong quasi-long-range magnetic order in both orbitals The spin and charge density waves in the dx2-y2 orbital are intertwined, as evidenced by their connected wavevectors 2QxS = QxD In this SDW phase, QµS = π/2 and the magnetic moments appear to better fit the spin-charge stripe order along a lattice direction The suppression of magnetic order is consistent with the emergent SC because of the singlet pairing formed in both orbitals Charge Order and Luttinger Liquid Behavior The charge order remains weak in both orbitals, with power exponents KµD ≳ 2, identifying a weak quasi-long-range CDW For ηe = 5/16, the system is in the LL phase where density correlations and spin correlations can be well fitted as power-law decay with power exponents close to 2 This numerical evidence on a quasi-one-dimensional system suggests the ground state as a LL The results indicate that increasing hole doping causes the SDW to be suppressed at ηe = 21/64 and a superconducting state emerges at the pressure of 21.6 GPa The study concludes that the ratio of interaction to hopping integral reduces moderately with increasing pressure, and a further comparative study supports the important role of this factor in the weakening of SC This suggests that interaction is also expected to suppress SC and give rise to a metallic state The results indicate that the ratio between hopping and interaction as the primary ingredient for the observations in Fig.

Mira: 5 The good agreements between this simulation and the original model indicate that the ratio of interaction to hopping integral, which reduces moderately with increasing pressure, should play a dominant role in the weakening of SC DFT calculations are performed using VASP with GGA exchange correlation potential (PBE) and DFT+U method for Ni atoms Projected tight-binding models are obtained through Wannier downfolding using WANNIER90 The ground state is determined by unbiased DMRG simulations implemented using the iTensor library, considering lattice width Ly = 1 and length up to Lx = 64 with open boundary conditions Data Availability Relevant data supporting the key findings of this study are available within the article and the Supplementary Information file The code that supports the plots within this paper is available from the corresponding author upon reasonable request Acknowledgments The work at Sun Yat-sen University was supported by various national and provincial funding sources, including the National Natural Sciences Foundation of China and the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices The computational resources were partially supported by the SongShan Lake HPC Center at Great Bay University Author Contribution D.

Kai: X.

Title and authors: Kai: To recap the main point of this paper, they are using the bilayer two-orbital Hubbard model to investigate how external pressure affects La three Ni two O seven’s superconducting properties.

Mira: They use DFT and DMRG to construct a quantum phase diagram where they see that superconductivity is suppressed by pressure and transitions into a Luttinger liquid above eighty GPa, which is what they observed experimentally with decreasing Tc.

Lev: The model itself incorporates specific parameters like the intermediate Hubbard repulsion U = four point zero eV and Hund’s coupling JH = zero point five eV, so it’s not just a generic model; it’s tailored to capture the physics of this specific nickelate.

Kai: They map out the competing orders, showing that for certain fillings, like three/eight minus eleven/thirty-two there is a strong spin density wave order in both orbitals without any static charge density wave order.

Mira: And they also show that at a lower filling of twenty-one/sixty-four a superconducting phase appears with interlayer SC in both orbitals and in-plane SC in the dz2 orbital, which happens alongside the suppression of the SDW <ref:2511.01801#pg2>.

Lev: It’s interesting to see how these competing orders interact; you can have magnetism and superconductivity appearing at different fillings depending on what you tune.

Kai: They also look at how pressure influences these phases, showing that increasing pressure eventually pushes it past eighty GPa into a Luttinger liquid state.

Mira: And they highlight the mechanism behind the weakening of SC, which is that the ratio of interaction to hopping integral changes moderately with increasing pressure.

Lev: So, if you were trying to run this on real hardware, knowing that pressure pushes it toward a Luttinger liquid state at eighty GPa tells you exactly where you need to be cautious about stability and error accumulation.

Kai: This whole paper is basically an investigation into the unusual pressure dependence of Tc in La three Ni two O seven using this specific theoretical framework.

Mira: It’s a detailed look at how the electronic structure changes under compression, which is essential context for understanding why things behave the way they do in this material.

Lev: We need to make sure our error analysis accounts for these phase transitions so we don't misinterpret a stable state as something it isn't.

The paper's summary: Kai: Now, what are the suggested improvements from this study? They suggest that they should focus on the ratio of interaction to hopping integral because that is a key factor in weakening superconductivity under pressure.

Mira: They suggest a comparative study focusing on how this ratio changes with increasing pressure to see if it's even more dominant than they currently imply.

Lev: From an engineering point of view, we need to test the sensitivity of the system to that parameter; if it’s that sensitive, our control parameters for pressure must be extremely precise.

Kai: They also suggest a comparative study supporting the idea that interaction is also expected to suppress SC and give rise to a metallic state.

Mira: That supports the idea that interaction itself has a role in suppressing superconductivity and driving it toward some metallic state under high pressure, which is something we need to keep in mind for our next theoretical setup.

Lev: So, if we are designing anything, we need to be careful because this paper flags that interaction doesn't just passively exist; it actively participates in destroying the SC.

Kai: They also suggest using the results from this study to guide synthesis towards optimal pressures for high Tc.

Mira: That means they can use the model to predict where they should stop applying pressure to get the best superconducting state, which is a useful predictive tool for material synthesis.

Lev: It’s about finding that sweet spot, but we need experimental validation because theory only gets you so far; the paper suggests this model will be a useful guide for guiding that search.

The paper's improvements: Kai: So to wrap up on the "Superconductivity of bilayer two-orbital Hubbard model for La three Ni two O seven under high pressure," the main implication is that we need to focus on how pressure affects this system.

Mira: They show that interaction is a primary ingredient for weakening superconductivity, and they also point out that the ratio between hopping and interaction as the primary ingredient for the observations in Fig five.

Lev: So, if we’re designing anything, we need to be careful because this paper flags that the ratio of interaction to hopping integral reduces moderately with increasing pressure.

Kai: This means interaction is expected to suppress SC and give rise to a metallic state, which is what they found in this specific nickelate.

Mira: So it’s a detailed look at how the electronic structure changes under compression, which is essential context for understanding why things behave the way they do in La three Ni two O seven.

Kai: This paper on the "Superconductivity of bilayer two-orbital Hubbard model for La three Ni two O seven under high pressure" shows that interaction is key to understanding the suppression of SC in this material.

Mira: They show that interaction itself has a role in suppressing superconductivity and driving it toward some metallic state under high pressure.

Lev: We need to make sure our error analysis accounts for these phase transitions so we don't misinterpret a stable state as something it isn't.

Conclusion: Kai: So we just finished looking at that paper, "Superconductivity of bilayer two-orbital Hubbard model for La three Ni two O seven under high pressure." Basically, they mapped out a quantum phase diagram using DFT and DMRG to see how pressure kills the superconductivity in this nickelate.

Mira: Exactly. They found that as pressure goes up, the transition temperature, Tc, drops until it basically turns into a Luttinger liquid above eighty GPa. That's a direct match for what they saw experimentally with decreasing Tc at lower pressures.

Lev: From an engineering standpoint, if you were trying to build a system that mimics this under compression, knowing it transitions to a Luttinger liquid above eighty GPa tells you exactly where the stability issues are going to become catastrophic for any actual measurement setup.

Kai: Right. And what they really dug into was the mechanism behind why it weakens—it came down to how much the ratio of interaction energy versus hopping energy changes as pressure increases, which is a moderate decrease.

Mira: That's crucial because it suggests that even a small change in that ratio under pressure has a big effect on destroying the superconducting state. It points to interaction itself being the driver for this suppression and pushing it toward a more metallic state.

Lev: If we were trying to run simulations of this on real hardware, that means we need very precise control over those hopping integrals and interaction potentials, because even moderate changes there are significant enough to push the system into a different phase entirely.

Kai: It’s interesting how they handled the competing orders too; for certain fillings, they found a spin density wave order exists without any static charge density wave order, which is pretty telling about the competition in that material.

Mira: And then at a lower filling, like twenty-one/sixty-four they see this superconducting phase emerge with interlayer SC in both orbitals and in-plane SC just for the dz2 orbital, and that happens while the spin density wave gets suppressed. That's a pretty neat interplay between magnetism and pairing.

Lev: The overhead for running those DMRG simulations on real hardware would be substantial if you have to sample that whole phase space, but their mapping helps us narrow down exactly which regions are the most physically relevant to explore first.

Kai: So, when we look at this "Superconductivity of bilayer two-orbital Hubbard model for La three Ni two O seven under high pressure," the main thing is that interaction isn't just background noise; it actively suppresses superconductivity and pushes it toward a Luttinger liquid state at eighty GPa.

Mira: And the key takeaway for us as theorists is that we need to pay close attention to how those ratios of interaction to hopping change under external stress, because that’s what dictates when the SC breaks down.

Lev: For us in error correction, it means we can't just assume a stable superconducting state will persist indefinitely; the pressure dependence shows you exactly where you need your stabilizers and gates to be most robust.

Kai: So, next time we look at a new arXiv paper, remember to check if they’re mapping out phase diagrams like this one—it gives you the context for what the underlying physics is trying to achieve.

Mira: And always ask yourself what assumptions they made about those interactions and hopping parameters; because that's where the real physics lives.

Lev: Then we figure out how much real-world noise or experimental uncertainty would push that theoretical prediction off track.

Kai: We’ll take a quick break, but when we come back, we’re diving into something totally different—looking at transmitter-device-independent quantum key distribution protocols. Stay with us.