Quantum Hall Edge Channels — 2D Skipping-Orbit 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 this 2D model works

Unlike a 3D perspective render of the same bar, this view draws each edge channel as a real semiclassical skipping orbit: a chain of exact semicircular cyclotron arcs (radius R_k ∝ the channel's guiding-centre offset) whose apex height and chord length satisfy the circle equation dx² + y² = R² at every sample — the bounce pattern is genuine circular-arc geometry, not a straight parametrized line.

Local half-width:   hw(x) = W0 - depth·exp(-x²/2σ²)
Transmission rule:  channel k (offset off_k) crosses iff  off_k < hw(0)
Landauer-Büttiker:  G = N·e²/h         Hall resistance:  R_xy = h/(N·e²)

The lower strip is a genuinely 2D-native parameter-space plot with no 3D counterpart at all: it sweeps the same transmission rule across every gate-voltage value to draw the full G(V_gate) staircase, then marks your current operating point live and leaves a trace of every voltage you've visited — the same physics (van Wees et al. 1988 conductance quantization) shown as a phase diagram instead of a real-space picture.

ν slider — bulk filling factor: how many edge channels exist far from the constriction.
Gate voltage slider — narrows the QPC gap; channels that no longer fit reflect off the boundary and skip straight back to their source — real quantized backscattering, not disorder.
Reverse field — flips which physical edge carries current in which direction.

Transmitted skipping orbit Backscattered skipping orbit Split gates (QPC)

Quantum Hall Edge Channels Through a Point Contact — 2D Skipping-Orbit View