Semiconductor Berry Curvature Calculator
Infer actual discrete plaquette curvature from independently computed principal Berry flux and oriented positive cell area; no eigenvector gauge reconstruction or phase unwrap.
Description
Discrete Berry curvature estimates normalize an independently computed plaquette flux by its oriented cell area.
Discrete Berry curvature estimates normalize an independently computed plaquette flux by its oriented cell area.1
The selected principal-flux branch and mesh conventions must already be established.
When to use Semiconductor Berry Curvature Calculator
Use this tool when you need to calculate the stated measurement summary or conditional model from matched observations. Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
How to use Semiconductor Berry Curvature Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedPlaquetteBerryFluxRadians, observedPlaquetteKSpaceAreas, following the field table and calculation rules below, then run the tool.
- Read observedBerryCurvatureByPlaquette. Use the output table and calculation rules below to interpret units, signs, crossings, and flags.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedPlaquetteBerryFluxRadians | Observed plaquette berry flux radians | list of number | Required |
| observedPlaquetteKSpaceAreas | Observed plaquette k space areas | list of number | Required |
Use nonempty aligned flux and positive k-space-area lists. Require every flux magnitude at most π and divide each signed flux by its area. No eigenvector computation, phase unwrapping, or mesh reconstruction occurs.
curvature_i=flux_i/area_i, abs(flux_i)≤π Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| observedBerryCurvatureByPlaquette | Observed berry curvature by plaquette | list of number |
{
"input": {
"observedPlaquetteBerryFluxRadians": [
0.2,
-0.4
],
"observedPlaquetteKSpaceAreas": [
2,
4
]
},
"output": {
"observedBerryCurvatureByPlaquette": [
0.1,
-0.1
]
}
}Limitations and assumptions
Measurements, branch identification, units, and model applicability must be independently established. Results do not supply universal material constants, a complete physical model, or operating-condition approval.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Numeric lists allow at most 10000 entries, subject to smaller tool-specific bounds above.
Alternative or Complementary methods
For a related task, use Semiconductor Chern Number Calculator: A discrete closed oriented mesh can provide a Berry-flux sum expressed in units of two pi. Its proximity to an integer is a numerical consistency screen requiring independent mesh and gap evidence. For a complementary step, use Semiconductor Dirac Point Energy Calculator: Two independently selected linear spectral branches can define a fitted crossing point. Their intersection is a model result and does not establish a protected Dirac node.
References
-
Semiconductor Berry Curvature Calculator — tool.io
Similar or alternative tools
- Semiconductor Chern Number Calculator
A discrete closed oriented mesh can provide a Berry-flux sum expressed in units of two pi. Its proximity to an integer is a numerical consistency screen requiring independent mesh and gap evidence.
- Semiconductor Dirac Point Energy Calculator
Two independently selected linear spectral branches can define a fitted crossing point. Their intersection is a model result and does not establish a protected Dirac node.