Quarter-metal phases in multilayer graphene: Ising-XY and annular Lifshitz transitions
Bibliographic record
Abstract
Recent experiments have uncovered a distinctive magnetic metal in lightly doped multilayer graphene, coined the quarter metal. This quarter metal consolidates all the doped carriers, originally distributed evenly across the 4 (or 12) Fermi surfaces of the paramagnetic state, into one expansive Fermi surface by breaking time-reversal and/or inversion symmetry. In this work, we map out a comprehensive mean-field phase diagram of the quarter metal in rhombohedral trilayer graphene within the four-dimensional parameter space spanned by the density ${n}_{e}$, interlayer electric potential $U$, external magnetic field parallel to the two-dimensional material plane ${B}_{\ensuremath{\parallel}}$, and Kane-Mele spin-orbit coupling $\ensuremath{\lambda}$. We found an annular Lifshitz phase transition and an Ising-XY phase transition and located these phase boundaries on the experimental phase diagram. The movement of the Ising-XY phase boundary offers insights into $\ensuremath{\lambda}$. Our analysis reveals that it moves along the line $\ensuremath{\partial}{n}_{e}/\ensuremath{\partial}{B}_{\ensuremath{\parallel}}\ensuremath{\sim}\ensuremath{-}0.5\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.28em}{0ex}}{\text{cm}}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}{\text{T}}^{\ensuremath{-}1}$ within the ${n}_{e}\text{\ensuremath{-}}{B}_{\ensuremath{\parallel}}$ parameter space when $\ensuremath{\lambda}=30\phantom{\rule{0.28em}{0ex}}\textmu{}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. Additionally, we estimated the in-plane spin susceptibility of the valley-Ising quarter metal ${\ensuremath{\chi}}_{{}_{\ensuremath{\parallel}}}\ensuremath{\sim}8\phantom{\rule{3.33333pt}{0ex}}\textmu{}\text{eV}\phantom{\rule{3.33333pt}{0ex}}{\text{T}}^{\ensuremath{-}2}$. Beyond these quantitative findings, two general principles emerge from our study: (1) The valley-XY quarter metal's dominance in the ${n}_{e}\text{\ensuremath{-}}U$ parameter space grows with an increasing number of layers due to the reduced valley-polarization variations within the Fermi sea. (2) Layer polarization near the band edge plays an important role in aiding the reentrance of the paramagnetic state at low density. The insights derived from the quarter-metal physics may shed light on the complex behaviors observed in other regions of the phase diagram.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".