Condensed Matter & Topological Physics

Quantum Hall Effect

Simulate Klaus von Klitzing's 1980 Nobel discovery: A 2D electron gas in high magnetic field $B$ exhibits quantized Hall resistance plateaus $R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu}$ with universal von Klitzing constant $R_K = 25812.807 \, \Omega$.

Filling Factor ν ν = 2 Plateau

Hall Resistance R_xy 12906.4 Ω

Longitudinal R_xx 0.0 Ω (Dissipationless)

2D Electron Gas Setup

Magnetic Field B 6.0 T

Electron Density n_s 3.0 × 10¹¹ cm⁻²

Visual Overlay

Show Skipping Orbit Topological Edge States

Show Quantized Landau Energy Levels

Show 2DEG Hall Bar Probe Badges

Controls

Quantized Hall Resistance & von Klitzing Constant

Cyclotron Frequency: ω_c = e B / m*
Landau Level Energies: E_n = ℏ ω_c (n + ½)
Quantized Hall Resistance: R_xy = h / (ν e²) = R_K / ν where R_K = 25812.807 Ω

Developer Reference

Core Algorithm & Standalone Script

// Quantum Hall effect plateau staircase engine
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// R_xy = R_K / nu, R_K = 25812.807 Ohm