Semiconductor Majorana Zero Mode Energy Calculator
Locate actual subgap eigenvalues nearest zero with ties/residual tolerance; near-zero energy does not identify Majorana modes, prove topology or exclude ordinary bound states.
Description
Subgap eigenvalues near zero are spectral candidates requiring independent physical interpretation.
Subgap eigenvalues near zero are spectral candidates requiring independent physical interpretation.1
Their proximity alone cannot distinguish Majorana modes from other bound states.
When to use Semiconductor Majorana Zero Mode 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 Majorana Zero Mode Energy Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedSubgapEigenvaluesEv, callerZeroModeEnergyToleranceEv, following the field table and calculation rules below, then run the tool.
- Read observedClosestZeroEnergyEv, closestAbsoluteSubgapEnergyEv, withinCallerZeroEnergyTolerance. 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 |
|---|---|---|---|
| observedSubgapEigenvaluesEv | Observed subgap eigenvalues eV | list of number | Required |
| callerZeroModeEnergyToleranceEv | Caller zero mode energy tolerance eV | number | Required |
Require a nonempty eigenvalue list and a nonnegative energy tolerance. Find the smallest absolute energy and retain every signed eigenvalue tied by exact equality. Compare that minimum inclusively with the tolerance.
emin=min(abs(E)); candidates={E:abs(E)=emin}; within=(emin≤tolerance) Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| observedClosestZeroEnergyEv | Observed closest zero energy eV | list of number |
| closestAbsoluteSubgapEnergyEv | Closest absolute subgap energy eV | number |
| withinCallerZeroEnergyTolerance | Within caller zero energy tolerance | boolean |
{
"input": {
"observedSubgapEigenvaluesEv": [
-0.01,
0.03,
-0.01
],
"callerZeroModeEnergyToleranceEv": 0.02
},
"output": {
"observedClosestZeroEnergyEv": [
-0.01,
-0.01
],
"closestAbsoluteSubgapEnergyEv": 0.01,
"withinCallerZeroEnergyTolerance": 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 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
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.