Exchange, correlation, and the effective mass <i>m</i>* of electrons in two‐dimensional layers calculated via a DFT‐based classical map
Bibliographic record
Abstract
Abstract Density functional theory uses the electron density n(r), instead of the electronic wavefunction. We side‐step the kinetic energy functional by constructing a thermodynamically equivalent classical map (CM). A classical Coulomb fluid whose zeroth‐order pair‐distribution function (PDF) g0(r) that agrees with the quantum g0, and interacting via a “Pauli exclusion potential” reproduces the thermodynamics of the electron fluid, when the classical‐fluid temperature Tcf is chosen optimally. This Tcf is chosen so that the correlation energy of the classical fluid is the Kohn–Sham correlation energy. Then, the PDFs of the classical fluid closely agree with the PDFs of the two‐dimensional (2D) and 3D uniform electron systems. Can we calculate sensitive Fermi‐liquid properties (e.g., quasiparticle mass m*, Landé g‐factor) of interacting electrons via this CM? Given the wide interest in the effective mass m* of electrons in 2D layers, we chose the 2D system for this study. Analytical and numerical results are used to define a partially regularized m* valid to logarithmic accuracy in the sense of Landau for the Hartree–Fock (H–F) approximation. The resulting H–F m* decreases linearly with the electron‐disk radius rs. The m* including correlation is calculated via a physically transparent formula. This uses the CM of the 2D PDF and its finite‐T exchange‐correlation free energy Fxc(T). Our results for m* fall well within the results from recent quantum Monte‐Carlo simulations at T = 0, and other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".