Semiconductor Valley Hall Conductivity Calculator
Quadrature of actual valley-restricted Berry curvature/k-space cells and occupations with caller signed convention/prefactor, not full topological Chern invariant or quantized conductivity claim.
Description
A valley-restricted conductivity estimate integrates sampled Berry curvature with k-space cell area and occupation.
A valley-restricted conductivity estimate integrates sampled Berry curvature with k-space cell area and occupation.1
Its sign and scale depend on the independently declared valley and conductivity convention.
When to use Semiconductor Valley Hall Conductivity 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 Valley Hall Conductivity Calculator and understand its results
- Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
- Enter observedValleyBerryCurvaturesM2, observedKSpaceCellAreasPerM2, observedOccupationFractions, callerConductivityPrefactorSiemens, following the field table and rules below, then run the tool.
- Read signedValleyHallConductivitySiemens. 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 |
|---|---|---|---|
| observedValleyBerryCurvaturesM2 | Observed valley berry curvatures m2 | list of number | Required |
| observedKSpaceCellAreasPerM2 | Observed k space cell areas per m2 | list of number | Required |
| observedOccupationFractions | Observed occupation fractions | list of number | Required |
| callerConductivityPrefactorSiemens | Caller conductivity prefactor siemens | number | Required |
Use aligned nonempty signed curvatures in square metres, positive k-space cell areas per square metre, occupation fractions in [0,1], and a positive prefactor in siemens. Sum curvature×cell area×occupation, multiply by prefactor, and divide by (2π)².
σ= prefactor×Σ(Ω_i×ΔkArea_i×occupation_i)/(2π)² Symbols follow the input and output meanings and the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| signedValleyHallConductivitySiemens | Signed valley hall conductivity siemens | number |
{
"input": {
"observedValleyBerryCurvaturesM2": [
1,
-2
],
"observedKSpaceCellAreasPerM2": [
2,
1
],
"observedOccupationFractions": [
1,
0.5
],
"callerConductivityPrefactorSiemens": 1
},
"output": {
"signedValleyHallConductivitySiemens": 0.025330295910584444
}
}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 observation lists allow at most 10,000 entries, subject to any smaller bounds stated above.
Alternative or Complementary methods
For a related review, 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. For a complementary step, use Semiconductor Valley Zeeman Splitting Calculator: Valley Zeeman analysis starts with independently assigned plus and minus spectral branches. A field-dependent fit of their signed difference can estimate an effective valley g factor.
References
Similar or alternative tools
- 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.
- Semiconductor Valley Zeeman Splitting Calculator
Valley Zeeman analysis starts with independently assigned plus and minus spectral branches. A field-dependent fit of their signed difference can estimate an effective valley g factor.