Quantum Hall Edge Channels Through a Point Contact

Sample

Filling factor ν (edge channels) 3

QPC gate voltage 0.0

Flow speed 1.0×

Transport Readouts

Transmitted channels N

3 / 3

QPC gap width

4.00 (a.u.)

Two-terminal conductance G = N·e²/h

3.00 e²/h (116.2 µS)

Hall resistance R_xy = h/(N·e²)

8.60 kΩ

How it works

In a strong perpendicular magnetic field, a 2D electron gas develops bulk Landau levels but the current is carried entirely by chiral edge channels — one-way conducting lines that skip along the sample boundary, immune to backscattering because there is no state moving the opposite way to scatter into:

Filling factor:  ν = n·h / (e·B)   (integer number of occupied edge channels)
Landauer-Büttiker:  G = N·e²/h   (N = number of channels that actually cross the device)
Hall resistance:    R_xy = h / (N·e²)

A quantum point contact (QPC) — two metal split gates deposited above the 2D gas — squeezes the conducting channel with an electrostatic potential. As the gate voltage increases, the constriction narrows and pinches off the edge channels one at a time, starting with the one running closest to the centre (largest offset from the physical edge), because it is the first to no longer fit inside the shrinking gap:

ν slider — sets how many edge channels exist far from the constriction (set by the bulk magnetic field / density).
Gate voltage slider — narrows the QPC gap; channels that do not fit are reflected straight back to their source instead of crossing to the drain — this is real, quantised backscattering, not disorder.
Reverse field — flips which physical edge carries current in which direction, exactly as reversing B flips the sign of the Hall voltage.

Sweeping the gate voltage while measuring conductance produces the famous staircase of flat plateaus at G = N·e²/h — first observed for ballistic point contacts by van Wees et al. (1988) and, in the quantum Hall regime specifically, used experimentally to selectively populate and detect individual edge channels.

Transmitted edge channel Backscattered edge channel Split gates (QPC)

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