Semiconductor Chern Number Calculator
Audit actual closed oriented Brillouin-mesh Berry flux sum against integer tolerance, raw residual preserved; rounding is not proof of converged/gapped Chern topology.
Description
A discrete closed oriented mesh can provide a Berry-flux sum expressed in units of two pi.
A discrete closed oriented mesh can provide a Berry-flux sum expressed in units of two pi.1
Its proximity to an integer is a numerical consistency screen requiring independent mesh and gap evidence.
When to use Semiconductor Chern Number 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 Chern Number Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedClosedMeshBerryFluxRadians, callerIntegerClosenessTolerance, callerClosedOrientedBrillouinMeshVerified, following the field table and calculation rules below, then run the tool.
- Read rawDiscreteChernSum, nearestIntegerChernCandidate, signedIntegerChernResidual, withinCallerIntegerTolerance. 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 |
|---|---|---|---|
| observedClosedMeshBerryFluxRadians | Observed closed mesh berry flux radians | list of number | Required |
| callerIntegerClosenessTolerance | Caller integer closeness tolerance | number | Required |
| callerClosedOrientedBrillouinMeshVerified | Caller closed oriented brillouin mesh verified | boolean | Required |
Require a true closed-oriented-mesh flag and tolerance in [0,0.5]. Sum the finite flux list, divide by 2π, round with JavaScript Math.round, and return raw value, candidate, signed residual, and inclusive tolerance result. Half ties round toward positive infinity; an empty flux list yields zero.
raw=Σflux/(2π); candidate=round(raw); residual=raw−candidate Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| rawDiscreteChernSum | Raw discrete chern sum | number |
| nearestIntegerChernCandidate | Nearest integer chern candidate | number |
| signedIntegerChernResidual | Signed integer chern residual | number |
| withinCallerIntegerTolerance | Within caller integer tolerance | boolean |
{
"input": {
"observedClosedMeshBerryFluxRadians": [
3.141592653589793,
3.141592653589793
],
"callerIntegerClosenessTolerance": 0.01,
"callerClosedOrientedBrillouinMeshVerified": true
},
"output": {
"rawDiscreteChernSum": 1,
"nearestIntegerChernCandidate": 1,
"signedIntegerChernResidual": 0,
"withinCallerIntegerTolerance": true
}
}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 Berry Curvature Calculator: Discrete Berry curvature estimates normalize an independently computed plaquette flux by its oriented cell area. The selected principal-flux branch and mesh conventions must already be established. For a complementary step, use Semiconductor Majorana Zero Mode Energy Calculator: Subgap eigenvalues near zero are spectral candidates requiring independent physical interpretation. Their proximity alone cannot distinguish Majorana modes from other bound states.
References
-
Semiconductor Chern Number Calculator — tool.io
Similar or alternative tools
- Semiconductor Berry Curvature Calculator
Discrete Berry curvature estimates normalize an independently computed plaquette flux by its oriented cell area. The selected principal-flux branch and mesh conventions must already be established.
- Semiconductor Majorana Zero Mode Energy Calculator
Subgap eigenvalues near zero are spectral candidates requiring independent physical interpretation. Their proximity alone cannot distinguish Majorana modes from other bound states.