Semiconductor Weyl Fermi Arc Length Calculator
Measure actual independently traced reciprocal-space Fermi-arc polyline and endpoint chord, not Weyl-node 3D separation, geodesy or identification of topology.
Description
A traced Fermi arc has a polyline length that can exceed its endpoint chord.
A traced Fermi arc has a polyline length that can exceed its endpoint chord.1
These two measurements summarize an independently ordered planar reciprocal-space trace.
When to use Semiconductor Weyl Fermi Arc Length Calculator
Use this tool when you need to reproduce the stated calculation from measured records or independently selected model inputs. Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
How to use Semiconductor Weyl Fermi Arc Length Calculator and understand its results
- Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
- Enter observedFermiArcPoints, callerIndependentlyOrderedSingleArcVerified, following the field table and rules below, then run the tool.
- Read observedFermiArcPolylineLength, observedArcEndpointSeparation. Use the output meanings below to interpret units, signs, flags, and any nested result fields.
- Correct reported input issues and run again. For a successful result, check the stated evidence coverage and assumptions before using it in your review.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedFermiArcPoints | Observed fermi arc points | numeric matrix | Required |
| callerIndependentlyOrderedSingleArcVerified | Caller independently ordered single arc verified | boolean | Required |
Use two or more explicit two-column points and true for an independently ordered single arc. Sum consecutive Euclidean segment lengths and compute the first-to-last distance. Topological identity and interpolation between sparse points are not inferred.
arcLength=Σ|point_(i+1)−point_i|; chord=|last−first| Symbols follow the input and output meanings and the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| observedFermiArcPolylineLength | Observed fermi arc polyline length | number |
| observedArcEndpointSeparation | Observed arc endpoint separation | number |
{
"input": {
"observedFermiArcPoints": [
[
0,
0
],
[
3,
0
],
[
3,
4
]
],
"callerIndependentlyOrderedSingleArcVerified": true
},
"output": {
"observedFermiArcPolylineLength": 7,
"observedArcEndpointSeparation": 5
}
}Limitations and assumptions
Matched measurement branch, material state, calibration, and conventions must be independently established. Results do not certify device performance or operating conditions.
Missing required fields, unknown fields, wrong types, and violated calculation rules are input issues. Numeric values must be finite; nonfinite results are rejected. Evidence arrays must be dense, with no missing cells. Numeric matrices are limited to 128 rows and 128 entries per row, with rectangularity required where stated.
Alternative or Complementary methods
For a related review, use Semiconductor Weyl Node Separation Calculator: Weyl-node separation is a displacement between independently identified nodes in one reciprocal-space frame. A directed vector preserves orientation alongside its Euclidean magnitude. For a complementary step, use Semiconductor Z2 Invariant Calculator: The two-dimensional Fu–Kane parity construction uses occupied Kramers-pair parities at four time-reversal-invariant momenta. It applies only after inversion and time-reversal symmetry and the occupied pairs have been established.
References
Similar or alternative tools
- Semiconductor Weyl Node Separation Calculator
Weyl-node separation is a displacement between independently identified nodes in one reciprocal-space frame. A directed vector preserves orientation alongside its Euclidean magnitude.
- Semiconductor Z2 Invariant Calculator
The two-dimensional Fu–Kane parity construction uses occupied Kramers-pair parities at four time-reversal-invariant momenta. It applies only after inversion and time-reversal symmetry and the occupied pairs have been established.