Quantum Hall Edge Channels Through a Point Contact

This simulator renders a Hall bar in the integer quantum Hall regime, where current is carried by discrete chiral edge channels rather than through the insulating bulk. A pair of split gates forms a quantum point contact in the middle of the bar; as you turn up the gate voltage the constriction narrows and channels are pinched off one by one, starting with the innermost. Every channel that still fits through the gap sails across to the opposite terminal untouched — edge states cannot backscatter into each other because there is no counter-propagating state to scatter into — while every channel that no longer fits is reflected cleanly back to its source. The live readouts track the transmitted channel count N, the resulting two-terminal conductance G = N·e²/h and the Hall resistance R_xy = h/(N·e²), reproducing the quantised conductance staircase measured in real point-contact experiments.