Excitonic instability of three-dimensional gapless semiconductors: Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>theory
Bibliographic record
Abstract
Three-dimensional gapless semiconductors with quadratic band touching, such as HgTe, $\ensuremath{\alpha}$-Sn, or ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, are believed to display a non-Fermi-liquid ground state due to long-range electron-electron interaction. We argue that this state is inherently unstable towards spontaneous formation of a (topological) excitonic insulator. The instability can be parameterized by a critical fermion number ${N}_{\mathrm{c}}$. For $N<{N}_{\mathrm{c}}$ the rotational symmetry is spontaneously broken, the system develops a gap in the spectrum, and features a finite nematic order parameter. To leading order in the $1/N$ expansion and in the static approximation, the analogy with the problem of dynamical mass generation in (2+1)-dimensional quantum electrodynamics yields ${N}_{\mathrm{c}}=16/[3\ensuremath{\pi}(\ensuremath{\pi}\ensuremath{-}2)]$. Taking the important dynamical screening effects into account, we find that ${N}_{\mathrm{c}}\ensuremath{\ge}2.6(2)$ and therefore safely above the physical value of $N=1$. Some experimental consequences of the nematic ground state are discussed.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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".