Quantum Hall Effect

2D electron gas in strong magnetic field at ultra-low temperature — Integer QHE model

R_xy = h / νe² ν = nh / eB E_N = ℏωc(N+½)
⚡

Landau Levels

In a perpendicular B field, allowed electron energies become discrete — like a 2D harmonic oscillator.

E_N = ℏωc(N+½)
🔢

Filling Factor ν

How many Landau levels are completely filled. Increasing B empties levels one by one.

ν = nh / eB
🔄

Chiral Edge States

Bulk states localize. Current flows via 1D edge channels — no backscattering, perfect conductance!

σxy = νe²/h
📐

Quantized Plateaus

R_xy locks to exact h/νe² at integer ν. Simultaneously R_xx → 0 on each plateau.

R_xy = h / νe²
2D Hall Bar & Chiral Edge Channels
Landau Level Fan
R_xy & R_xx vs Magnetic Field
Controls
Magnetic field B8.0 T
2D density n4.0 × 10¹&sup5; m²
Temperature T1.5 K
Drive current I5.0 μA
Live Readouts
Filling factor ν
2.00
Plateau index
2
Rxy (Hall)
12.91 kΩ
Rxx (long.)
≈ 0 Ω
VHall
64.6 mV
ℏωc
1.39 meV
σxy
2 × e²/h
Cyclotron freq.
2.11 THz
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