Inductance of Wire | Landau Length Calculator

Use this landau length calculator to calculate landau length using electronic charge,permittivity of vaccum,Boltzman constant and electronic temperature

Inductance of Wire Calculator
Electronic Charge
Permittivity Of Vacuum
Boltzmann Constant
Electron Temperature
Landau Length: {{landauLengthResult()}}

How to use Landau Length Calculator?

Step 1 - Enter the Electronic Charge

Step 2 - Enter the Permittivity Of Vacuum

Step 3 - Enter the Boltzmann Constant

Step 4 - Enter the Electron Temperature

Step 5 - Calculate Landau Length

Landau Length Calculator Formula:

lL = $e^2$ / (4πεokBTe)

Where,

lL = Landau Length

e = Electronic Charge

εo = Permittivity Of Vacuum

kB= Boltzmann Constant

Te= Electron Temperature

Frequently Asked Questions

Landau length is a fundamental length scale in quantum magnetism that characterizes the spatial extent of electron wavefunctions in strong magnetic fields. It represents the size of Landau level wavefunctions and becomes important when the magnetic field is strong enough that quantum effects dominate over classical motion. Landau length decreases with increasing magnetic field and electron temperature, determining the regime where integer quantum Hall effect becomes observable.

How does electron temperature affect Landau length calculations?

Landau length is inversely proportional to the square root of electron temperature (proportional to 1/√T). Higher temperatures increase thermal energy and electron momentum, requiring stronger magnetic fields to confine electrons to the same spatial extent. This temperature dependence is critical for understanding quantum behavior in different experimental regimes.

When should I use Landau length in quantum magnetism analysis?

Use Landau length when analyzing quantum Hall effects, cyclotron resonance, or magnetic field effects on 2D electron systems. It’s essential for understanding when quantum mechanical effects dominate over classical behavior. If the system size is comparable to or smaller than Landau length, quantum quantization becomes important. It’s particularly relevant in condensed matter physics and semiconductor physics.

What are the assumptions underlying Landau length theory?

Landau length assumes a uniform, strong magnetic field perpendicular to the electron motion. It applies to non-interacting electrons in 2D systems with parabolic energy dispersion. Real materials show deviations due to disorder, electron-electron interactions, and non-parabolic energy bands. The theory is most accurate for clean, high-purity samples in high magnetic fields.

Wire inductance depends on the geometry and surrounding field configuration. In quantum regime calculations, Landau length describes how confined electrons contribute to magnetic properties. Understanding length scales is crucial for predicting inductance in microscopic systems and superconductors where quantum effects become dominant.

Physical Basis & References

This calculator applies Quantum Magnetism and Landau Level Theory:

$$l_L = \sqrt{\frac{\hbar}{eB}} = \sqrt{\frac{\varepsilon_0 e k_B T_e}{e^2 \cdot \text{effective field}}}$$

Key Physics Principles:

  • Landau Quantization - Electron energy levels quantize in magnetic fields
  • Cyclotron Motion - Electrons orbit with characteristic size Landau length
  • Quantum Hall Effect - Integer/fractional plateaus emerge when system size ~ Landau length
  • Magnetic Length Scale - Determines spatial extent of quantum wavefunctions

Key Assumptions:

  • Two-dimensional electron system
  • Uniform perpendicular magnetic field
  • Parabolic energy dispersion
  • Non-interacting electrons (mean-field approximation)
  • Strong magnetic field regime

Typical Range of Values:

  • Landau length: 5 nm (high field) to 100 nm (low field)
  • Magnetic field: 0.1 T to 100 T
  • Electron temperature: 1 K to 100 K
  • System dimensions: 1 μm to 100 μm

Further Reading:

  • Ashcroft, N.W. & Mermin, N.D. (1976). Solid State Physics. Holt, Rinehart and Winston.
  • Landau, L.D. & Lifshitz, E.M. (1977). Quantum Mechanics, 3rd Edition. Pergamon Press.
  • Integer Quantum Hall Effect - Nobel Prize in Physics 1985 documentation

Conclusion

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