Quantum Point Contact

Gate voltage V_g -1.40 V

Flow speed 1.0×

Channel width W

–

Open modes N

–

Conductance G

–

G / G₀

–

How it works

Two metal gate electrodes sit above a two-dimensional electron gas (2DEG) formed at a GaAs/AlGaAs heterostructure interface. A negative voltage on the gates depletes electrons underneath them, squeezing the 2DEG into a narrow constriction — the quantum point contact (QPC). When the constriction is comparable to the electron's Fermi wavelength, its width no longer looks continuous to the electrons: only a whole number of transverse standing-wave modes fit across it.

N = floor(k_F · W / π)
G = N · G₀,  G₀ = 2e²/h ≈ 77.5 μS

Each fully open mode is a perfect ballistic channel and contributes exactly one quantum of conductance G₀ = 2e²/h — the Landauer formula. Because N can only be an integer, sweeping the gate voltage (and hence the width) produces a staircase of flat conductance plateaus rather than a smooth ramp, exactly as van Wees et al. first measured in 1988.

Gate voltage — more negative depletes the 2DEG further, narrowing the constriction and closing modes one at a time.
Flow speed — visual playback rate of the electron stream; does not affect the physics.
Channel width / open modes — the live geometric width and the resulting integer mode count feeding the Landauer formula.

Real-world relevance: QPCs are the workhorse building block of mesoscopic electronics — used as tunable coulomb-blockade barriers, charge sensors for spin qubits, and the cleanest table-top demonstration that electrical conductance is fundamentally quantized.

2DEG electrons Open mode lane Gate electrode

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Quantum Point Contact — Conductance Quantization