Band structure and magnetotransport of a two-dimensional electron gas in the presence of spin-orbit interaction
Bibliographic record
Abstract
The band structure and magnetotransport of a two-dimensional electron gas (2DEG), in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of the spin-orbit interaction and of a perpendicular magnetic field, is investigated. Exact and approximate analytical expressions for the band structure are obtained quantum mechanically and used to calculate the density of states (DOS) and the longitudinal magnetoresitivity assuming a Gaussian type of level broadening. The interplay between the Zeeman coupling and the two terms of the SOI is discussed. If the strengths $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, of the RSOI and DSOI, respectively, are equal and the $g$ factor vanishes, the two spin states are degenerate and a shifted Landau-level structure appears in agreement with recent semiclassical results. With the increase of the difference $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\beta}$, a beating pattern of the DOS and of the Shubnikov-de Haas oscillations appears distinctly different from that occurring when one of these strengths vanishes. For $\ensuremath{\alpha}⪢\ensuremath{\beta}$ or $\ensuremath{\alpha}⪡\ensuremath{\beta}$ the peaks in one wrap of the beating pattern occur at even filling factors of the 2DEG while in the next wrap they occur at odd filling factors. For $\ensuremath{\alpha}\ensuremath{\approx}\ensuremath{\beta}$ this transition occurs only if the spin splitting is larger than half the Landau energy.
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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".