Semiconductor Dirac Point Energy Calculator
Fit actual independently selected linear Dirac branches and report their intersection, not reference Fermi energy or a proof of protected Dirac crossing.
Description
Two independently selected linear spectral branches can define a fitted crossing point.
Two independently selected linear spectral branches can define a fitted crossing point.1
Their intersection is a model result and does not establish a protected Dirac node.
When to use Semiconductor Dirac Point Energy 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 Dirac Point Energy Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedUpperDiracBranchK, observedUpperDiracBranchEnergyEv, observedLowerDiracBranchK, observedLowerDiracBranchEnergyEv, following the field table and calculation rules below, then run the tool.
- Read fittedDiracPointK, fittedDiracPointEnergyEv. 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 |
|---|---|---|---|
| observedUpperDiracBranchK | Observed upper dirac branch k | list of number | Required |
| observedUpperDiracBranchEnergyEv | Observed upper dirac branch energy eV | list of number | Required |
| observedLowerDiracBranchK | Observed lower dirac branch k | list of number | Required |
| observedLowerDiracBranchEnergyEv | Observed lower dirac branch energy eV | list of number | Required |
Fit both aligned branch datasets separately with free intercepts. Require distinct fitted slopes, solve their line intersection, and evaluate the upper fitted line there. The intersection can lie outside both measured ranges; this tool does not reject extrapolated intersections.
The regression helper accepts 2–10000 aligned finite pairs with nonzero predictor variance. It fits ordinary least squares with a free intercept using shifted coordinates; samples need not be sorted unless this tool additionally requires it. R² is clamped to [0,1] and is one for constant responses. Transformed fits use the stated log or reciprocal predictor/response basis; R² is a fit summary rather than a confidence interval.
k=(alower−aupper)/(bupper−blower); E=aupper+bupper×k Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedDiracPointK | Fitted dirac point k | number |
| fittedDiracPointEnergyEv | Fitted dirac point energy eV | number |
{
"input": {
"observedUpperDiracBranchK": [
0,
1,
2
],
"observedUpperDiracBranchEnergyEv": [
1,
2,
3
],
"observedLowerDiracBranchK": [
0,
1,
2
],
"observedLowerDiracBranchEnergyEv": [
3,
2,
1
]
},
"output": {
"fittedDiracPointK": 1,
"fittedDiracPointEnergyEv": 2
}
}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 Dirac Fermi Velocity Calculator: A band-energy slope with respect to wavevector gives a signed group-velocity scale under a matched linear-branch convention. Using joules, inverse metres, and the supplied reduced Planck constant keeps the SI conversion explicit. 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
Similar or alternative tools
- Semiconductor Dirac Fermi Velocity Calculator
A band-energy slope with respect to wavevector gives a signed group-velocity scale under a matched linear-branch convention. Using joules, inverse metres, and the supplied reduced Planck constant keeps the SI conversion explicit.
- 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.