Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors

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

Kai: Today's paper: "Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors".

Mira: The gist: The study numerically investigates how weak, random, spatial velocity modulation in two-dimensional massless Dirac materials acts as quenched gravitational disorder (QGD),

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

Title and authors: Kai: Let's talk about the authors and the title of this paper, "Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors." It sounds pretty technical, but it’s addressing a specific problem in these Dirac materials.

Mira: The authors are Sayed Ali Akbar Ghorashi, Jonas F. Karcher, Seth M. Davis and Matthew S Foster at William and Mary, Karlsruhe Institute of Technology and Rice University respectively. They bring different expertise to this problem of disorder in quantum systems.

Lev: I'm interested in seeing if the results they got are robust enough for actual error correction protocols we're designing for superconducting circuits.

Kai: The title suggests that the core idea is about criticality across the energy spectrum, which points toward finding universal behavior even when you introduce this kind of artificial gravitational lensing effect via QGD.

Mira: What this means in simple terms is that they are showing how adding random spatial velocity variations—this QGD—doesn't just scatter things randomly; it forces most of the states into a specific, highly structured critical state.

Lev: So, if I translate that to hardware, it suggests we might need to model the noise not just as simple uncorrelated scattering but as this kind of spatially correlated velocity modulation.

The paper's summary: Kai: Now let's get into the summary of what they actually found in "Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors." They are studying five variants of velocity disorder incorporating three different local deformations of the Dirac cone: flattening or steepening, pseudospin rotations, and nematic deformation.

Mira: The key finding they report is that critical-state stacking occurs for sufficiently weak disorder in all five models, which means almost every single variant shows this behavior under small amounts of this QGD.

Lev: That's a strong statement because it implies the underlying physics causing this stacking isn't just an artifact of one specific type of deformation they chose to study.

Kai: They also noted that the stacking actually improves in models (b) and (d) as the disorder gets stronger, meaning more states become quantum-critical with identical, universal spectra throughout a wider energy range.

Mira: That robustness in model (d), which only uses pure nematic deformations of the Dirac cone, is particularly interesting because it suggests this effect might be quite fundamental to how the system handles spatial inhomogeneity.

The paper's improvements: Kai: Regarding improvements, they suggest that models (a) and (c), which use local flattening or steepening of the cone, are most susceptible to strong disorder effects, showing supercritical states at low- and high-energies for increasing randomness.

Mira: They point out that model (d), focusing only on pure nematic deformations, exhibits this robust behavior with critical stacking across more of the spectrum than the others.

Lev: If we look at running this on real systems, it tells us that the type of geometric deformation matters a lot for how stable this critical state is against increasing disorder.

Kai: The generic model (e) shows intermediate behavior, with a robust energy swath with critical stacking but also supercritical behavior at low energies as disorder increases.

Mira: They also calculated an effective energy scale zero which they found decreases slightly with increasing disorder strength lambda, and this decrease qualitatively matches some data from cuprate superconductors <ref:1903.11086#pg3>.

Conclusion: Kai: So, to wrap up, the paper on "Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors" uncovers a third instance of quantum-critical wave function stacking specifically due to QGD. This suggests it could offer a simple explanation for the division between plane-wave-like and spatially inhomogeneous LDOS fluctuations seen at different energies in high-Tc cuprates.

Mira: The best qualitative match to what they’re seeing in cuprate studies is found in model (b), which incorporates local rotations of the pseudospin axes relative to the coordinate axes. And we see robust stacking that actually increases with increasing disorder strength in both model (b) and model (d).

Lev: For my work on error correction, this tells us that if we're dealing with a system exhibiting this stacking, we should expect the critical behavior to become more pronounced as the disorder gets stronger.

Kai: And they conclude by noting that a kink in the density of states observed right at the threshold of critical stacking might actually arise due to quasiparticle-quasiparticle interactions.

Mira: We’re left wondering if this kind of robust stacking, especially in model (d), is something we could use to improve superconductivity in a self-consistent calculation of the gap.

Lev: I'm still focused on whether that crossover scale zero remains finite or vanishes when you take the system size L to infinity, because that would tell us if there's a transition between ballistic and this quantum-critical stacked behavior <ref:1903.11086#pg3>.

Kai: Right, so we’ve looked at how QGD creates these critical stacks in Dirac materials, and the next step is figuring out what happens when you take the system to an infinite size.