Charge transport in graphene-based mesoscopic realizations of Sachdev-Ye-Kitaev models
Bibliographic record
Abstract
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio $p$ between the number of transverse modes in the lead $M$ and the number of the fermion degrees of freedom $N$ on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct $\sqrt{p}$ and $1/\sqrt{p}$ dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias $U$. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to $1/\sqrt{T}$ for bias energy $eU$ smaller than temperature scale ${k}_{B}T$. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".