Spin- and valley-dependent analysis of the two-dimensional low-density electron system in Si MOSFETs
Bibliographic record
Abstract
The two-dimensional electron system (2DES) in $\mathrm{Si}$ metal-oxide field-effect transistors consists of two distinct electron fluids interacting with each other. We calculate the total energy as a function of the density $n$ and the spin polarization $\ensuremath{\zeta}$ in the strongly correlated low-density regime, using a classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge terms. The ten distribution functions arising from spin and valley indices are calculated to obtain the total free energy, the chemical potential, the compressibility, and the spin susceptibility. The $T=0$ results are compared with the two-valley quantum Monte Carlo (QMC) data of Conti and Senatore [Europhys. Lett. 36, 695 (1996)] (at $T=0$, $\ensuremath{\zeta}=0$) and found to be in excellent agreement. Unlike in the one-valley 2DES, it is shown that the unpolarized phase is always the stable phase in the two-valley system, right up to Wigner crystallization at ${r}_{s}\ensuremath{\sim}40$. Hence ${g}^{*}$ is insensitive to the spin polarization and to the density. The compressibility and the spin-susceptibility enhancement calculated from the free energy validate a simple approach to the two-valley response based on coupled-mode formation. The local-density approximation of density-functional theory is shown to fail, especially near ${r}_{s}=1$, even though the 2DES is uniform. The spin-susceptibility enhancement calculated from the coupled-valley response and directly from the two-valley energies is discussed. The three methods, QMC, CHNC, and coupled-mode theory, agree closely. Our results contain no ad hoc fit parameters and lead to general agreement with available experimental results.
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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".