Condensed matter physics

The quantum Hall effect

Sweep the filling factor ν through the Landau levels of a two-dimensional electron gas, watch the chiral edge channels, and verify the Hall resistance $R_{xy} = h/(\nu e^2)$ with plateaus at $h/e^2 \approx 25{,}8\ \mathrm{k\Omega}$ .

Research

Equipment

3D figure of Landau levels and edge flow in the 2D electron gas
“Filling factor ν” slider
“Temperature (relative)” and “Model parameter” sliders
“Time” slider for the edge-current animation and the “Pause” button
Readout lines for the Hall plateau and normalized resistance

Procedure

Sweep ν through the Landau levels
Drag “Filling factor ν” from 0 to 100: each time the Fermi level crosses a Landau level, the Hall resistance steps to a new value. Read the plateau index ν on the label and compare with $R_{xy} = h/(\nu e^2)$ ; between steps $R_{xy}$ stays fixed — the plateau.
Vary the temperature and the plateau sharpness
Raise “Temperature (relative)” and watch the plateau smear out; lower it to see the sharp step with $R_{xx} \to 0$ . Explain: thermal activation lets carriers scatter between Landau levels, destroying the perfect quantization.
Watch the one-way edge channels
Use “Time” to run the animation or “Pause”: carriers flow along the sample edge in one direction only (chiral); with no path backward, backscattering is suppressed. Relate this to $R_{xx} \approx 0$ on the ideal plateau and the standard value $h/e^2 \approx 25{,}8\ \mathrm{k\Omega}$ .

Simulation

Experiment history

Edwin Hall discovered his eponymous effect in 1879 in a metal foil under a magnetic field. A century later, in 1980, Klaus von Klitzing measured the Hall resistance of a two-dimensional electron gas in a MOSFET at high field and low temperature: instead of a straight line,

R_{xy}

showed plateaus at

h/(\nu e^2)

accurate to parts per billion — a discovery awarded the 1985 Nobel prize and used to redefine the ohm. In 1982 Daniel Tsui and Horst Störmer (on samples grown by Arthur Gossard) found a plateau at ν = 1/3 — the fractional quantum Hall effect — explained by Robert Laughlin via a strongly correlated ground state; the three shared the 1998 Nobel. The chiral edge states in this simulation are the core picture of both effects.

Related physicists

Paul Dirac Richard Feynman Klaus von Klitzing Robert Betts Laughlin Horst Ludwig Störmer Daniel Chee Tsui

Equipment

Procedure

Simulation

Experiment history

Related physicists

Related library topics