Bibliographic record
Abstract
Abstract We calculate the AC optical response of a line node semimetal with emphasis on characteristic behaviours which can be used to distinguish them from point node materials such as Dirac and Weyl semimetals. The interband optical background at zero temperature displays a flat region at small photon energies ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mo mathvariant="normal">Ω</mml:mo> </mml:mstyle> </mml:math> ) analogue to the universal background seen in graphene. However, in contrast to graphene, the height of the constant region is not universal but depends inversely on the Fermi velocity of the charge carriers and directly on the radius ( b ) in momentum space of the nodal circle. The parameter b is a defining energy scale and determines the range of photon energy over which the flat response persists. At high energies <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mo mathvariant="normal">Ω</mml:mo> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> <mml:mi>b</mml:mi> </mml:mstyle> </mml:math> , the interband response becomes linear in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mo mathvariant="normal">Ω</mml:mo> </mml:mstyle> </mml:math> in agreement with the case for 3D-Dirac fermions with point node. The optical spectral weight contained in the interband or Drude conductivity shows the same two distinct regimes. At low temperature ( T ) (chemical potential ( μ )), it rises linearly with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>T</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>μ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> and is proportional to b . At high temperature, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>T</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>μ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> , a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mstyle> <mml:mo stretchy="false">(</mml:mo> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mstyle> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> law is obtained, which is independent of b . At T = 0, the Lorentz number takes on the conventional value <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mi>o</mml:mi> </mml:msub> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mstyle> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mi>e</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mstyle> </mml:mstyle> </mml:math> for all values of μ . It increases with increasing temperature to reach a first plateau of 2.4 L o provided <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>T</mml:mi> <mml:mo>></mml:mo> <mml:mi>μ</mml:mi> </mml:mstyle> </mml:math> but <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>μ</mml:mi> <mml:mo>≪</mml:mo> <mml:mi>b</mml:mi> </mml:mstyle> </mml:math> . At high temperature, T > b , a second plateau of height 4.2 L o emerges. The first plateau is characteristic of 2D-Dirac while the second corresponds to 3D-Dirac. The thermopower as a function of temperature also shows an evolution from a 2D to 3D behaviour.
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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 | 0.000 | 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) | 0.004 | 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".