Quantum magnetic oscillations in Weyl semimetals with tilted nodes
Bibliographic record
Abstract
A Weyl semimetal (WSM) is a three-dimensional topological phase of matter where pairs of nondegenerate bands cross at isolated points in the Brillouin zone called Weyl nodes. Near these points the electronic dispersion is gapless and linear. A magnetic field $B$ changes this dispersion into a set of positive and negative energy Landau levels which are dispersive along the direction of the magnetic field only. In this set, the $n=0$ Landau level is special since its dispersion is linear and unidirectional. The presence of this chiral level distinguishes Weyl from Schr\"odinger fermions. In this paper we study the quantum oscillations of the orbital magnetization and magnetic susceptibility in Weyl semimetals. We generalize earlier works on these de Haas--van Alphen oscillations by considering the effect of a tilt of the Weyl nodes. We study how the fundamental period of the oscillations in the small $B$ limit and the strength of the magnetic field ${B}_{1}$ required to reach the quantum limit (i.e., where the Fermi level is lying in the chiral level) are modified by the magnitude and orientation of the tilt vector $\mathbf{t}$. We show that the magnetization from a single node is finite in the $B\ensuremath{\rightarrow}0$ limit. Its sign depends on the product of the chirality and sign of the tilt component along the magnetic field direction. We also study the magnetic oscillations from a pair of Weyl nodes with opposite chirality and with opposite or identical tilt. Our calculation shows that these two cases lead to a very different behavior of the magnetization in the small and large $B$ limits. We finally consider the effect of an energy shift $\ifmmode\pm\else\textpm\fi{}{\mathrm{\ensuremath{\Delta}}}_{0}$ of a pair of Weyl nodes on the magnetic oscillations. We assume a constant density of carriers so that both nodes share a common Fermi level and the density of carriers is constantly redistributed between the two nodes as the magnetic field is varied. Our calculation can easily be extended to a WSM with an arbitrary number of pairs of Weyl nodes.
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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 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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".