Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice

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: "Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice".

Mira: Here's the gist of the paper. The gist: The study investigates whether a pair density wave (PDW) state or distinct superconducting (SC) state emerges upon doping in the Emery model, revealing that for negative oxygen-oxygen hopping, SC pairing is dominant between neighboring oxygen sites with a dxy-wave symmetry rather than the expected dx2−y2 wave Model and Method The research employs a density-matrix renormalization group (DMRG) study to examine the Emery model on two-leg square cylinders to determine if the same PDW state or distinct SC state emerges upon doping and what the associated pairing symmetry is.

Kai: The model, also known as the three-band Hubbard model, considers a square lattice of copper and oxygen atoms where copper sites are represented by a single 3dx2−y2 orbital and each oxygen site has two active 2p orbitals.

Mira: Kinetic frustration is introduced by changing the sign of oxygen-oxygen hopping term tpp, which leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model.

Kai: The study focuses on two-leg cylinders with width Ly = 2 and length up to Lx=96, considering hole densities of δ = 1/12 and 1/8.

Title and authors: Kai: So we're looking at a paper called "Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice," right? It’s by Hong-Chen Jiang and Thomas Peter Devereaux.

Mira: Yeah, that title tells you the main thing right away: they are investigating whether a pair density wave state or some distinct superconducting state shows up when you dope this specific Emery model.

Kai: It’s really about seeing if this system develops that spatially modulated order parameter we call a pair density wave, which is something we haven't seen conclusively in cuprates yet.

Mira: And the authors are using a density-matrix renormalization group study to see if they get that PDW state or just some other kind of superconducting state and what the pairing symmetry looks like.

Lev: From an engineering standpoint, a DMRG study on two-leg square cylinders tells us about the complexity of simulating these higher dimensional systems without introducing too much error in the hardware setup.

Kai: Right, so they’re using that DMRG method to probe this Emery model on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites.

Mira: The implication is that by changing the sign of that oxygen-oxygen hopping, which introduces kinetic frustration, they are looking at how that affects the magnetic exchange and charge transfer energy.

Lev: That change in kinetic frustration is what allows them to look at a system where the Cu-Cu antiferromagnetic exchange gets much reduced, which is interesting for how we model those strong correlations.

The paper's summary: Kai: Okay, so the paper summarizes their findings on this pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice.

Mira: They found that when you look at the ground state phase diagram at doping delta equals one/eight if you keep the oxygen-oxygen hopping Vpp not strongly attractive, the system is consistent with a PDW state <ref:2309.11786#pg3>.

Kai: And in this PDW phase, they see power-law and mutually commensurate correlations for both charge density wave and spin density wave alongside that superconducting correlation.

Mira: The key thing they pointed out is that the SC correlations oscillate periodically in real space, but their spatial average vanishes, meaning it’s not a simple uniform state.

Lev: That oscillating correlation pattern suggests quasi-long-range order for the charge and spin channels because of those power-law decays they measure.

Kai: And regarding the superconductivity itself, they found that Cooper pairing prominently emerges between adjacent oxygen sites rather than between neighboring Cu sites.

Mira: This is a big finding because it means the pairing symmetry is consistent with dxy rather than the dxtwo-y2 wave we usually see in cuprates.

Lev: If we were building hardware to realize this, that means our coupling scheme has to strongly favor those oxygen-oxygen interactions over the direct copper-copper ones.

The paper's improvements: Kai: Now for the improvements they suggest with this work on the pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice.

Mira: They suggest that when you incorporate moderate near-neighbor interactions, specifically an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged.

Kai: And they also note that this attractive Vpp leads to a pronounced divergence in the PDW susceptibility, which is a very strong signal for that ordering.

Lev: From an error correction perspective, that divergence in susceptibility would mean the system is extremely sensitive to small perturbations, which makes running it on real hardware pretty challenging because you need very precise control.

Mira: Further increase in that attractive Vpp allows the system to give way to an unconventional d-wave superconductivity where those PDW signatures get much suppressed.

Kai: So they suggest a pathway where tuning the oxygen-oxygen interaction can drive the system from a PDW state into a conventional d-wave superconducting state.

Lev: That transition point, where the PDW signatures get suppressed, would be a crucial benchmark for testing any error correction protocol designed to handle these competing orders.

Conclusion: Kai: So to wrap up on this paper about pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice.

Mira: The main implication is that the system’s ground state is strongly aligned with the characteristics of a PDW state, showing quasi-long-range order and strong susceptibility.

Kai: And that Cooper pairing prominently emerges between adjacent oxygen sites, which points to a dxy symmetry instead of the dxtwo-y2 we usually expect.

Mira: This work also shows that there's both a gapless charge mode and a gapless spin mode present in this system, which is indicated by the central charge being approximately given by c equals one point nine five or c equals two point zero depending on the parameters <ref:2309.11786#pg1>.

Lev: For real hardware, that presence of both gapless modes means we’re dealing with complex dynamics that require careful modeling to ensure any error correction protocol can actually capture those excitations correctly and not just miss them in the simulation.

Kai: Exactly, so tuning the oxygen-oxygen interaction lets you switch between these different phases like PDW and d-wave superconductivity.

Mira: It’s a detailed look at how kinetic frustration can change the fundamental pairing symmetry of these correlated electron systems.

Lev: The whole point is to understand the real physical constraints on how we build those exotic materials and see what kind of excitations we have to deal with when trying to engineer them for quantum computation.