Validity of the two-component model of bilayer and trilayer graphene in a magnetic field
Bibliographic record
Abstract
The eigenstates of an electron in the chiral two-dimensional electron gas (C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene is a spinor with four or six components, respectively. These components give the amplitude of the wave function on the four or six carbon sites in the unit cell of the lattice. In the tight-binding approximation, the eigenenergies are thus found by diagonalizing a $4\ifmmode\times\else\texttimes\fi{}4$ or a $6\ifmmode\times\else\texttimes\fi{}6$ matrix. In the continuum approximation where the electron wave vector $k\ensuremath{\ll}1/{a}_{0},$ with ${a}_{0}$ the lattice constant of the graphene sheets, a common approximation is the two-component (or ``two-band'') model1 where the eigenstates for the bilayer and trilayer systems are described by a two-component spinor that gives the amplitude of the wave function on the two sites with low energy $|E|\ensuremath{\ll}{\ensuremath{\gamma}}_{1}$ where ${\ensuremath{\gamma}}_{1}$ is the hopping energy between sites that are directly above one another in adjacent layers. The two-component model has been used extensively to study the phase diagram of the C2DEG in a magnetic field as well as its transport and optical properties. In this paper, we use a numerical approach to compute the eigenstates and Landau level energies of the full tight-binding model in the continuum approximation and compare them with the prediction of the two-component model when the magnetic field or an electrical bias between the outermost layers is varied. Our numerical analysis shows that the two-component model is a good approximation for bilayer graphene in a wide range of magnetic field and bias but mostly for Landau level $M=0.$ The applicability of the two-component model in trilayer graphene, even for level $M=0,$ is much more restricted. In this case, the two-component model fails to reproduce some of the level crossings that occur between the sublevels of $M=0.$
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.005 | 0.002 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".