Ionic screening of charged impurities in electrolytically gated graphene
Bibliographic record
Abstract
We present a model for dual-gated, single-layer graphene, with a back gate separated by a layer of oxide, and the top gate potential applied through a thick layer of liquid electrolyte that contains mobile ions in a diffuse layer, described in the Debye-H\"uckel approximation, which is separated from graphene by a charge-free Stern layer. After deriving a nonlinear equation for the average charge carrier density in graphene in terms of the gate potentials, we use the Green's function of the Poisson equation to express the fluctuating part of the electrostatic potential in the plane of graphene in terms of the distribution function for fixed charged impurities in the oxide. By using both the Thomas-Fermi and the random phase approximations of graphene's response at nonzero temperature, we show that the presence of mobile ions in the electrolyte significantly increases graphene's screening ability of the in-plane potential for a single impurity, accentuates Friedel oscillations in that potential, and gives rise to a linear plasmon dispersion in doped graphene at long wavelengths. In the case of multiple charged impurities in the oxide, the increasing ion concentration in the electrolyte causes a reduction in the autocorrelation function of the fluctuating in-plane potential when the impurities are uncorrelated. However, when the impurities are correlated, the relative effect of the increased ion concentration in the electrolyte is drastically reduced, while the autocorrelation function in this case takes negative values in a range of interimpurity distances.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".