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title: "Integer quantum Hall effect: a plateau became a resistance reference"
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Materials · Measurements · Explanation

# Integer quantum Hall effect: a plateau became a resistance reference

Why was a flat Hall-resistance interval more informative than a single crossing of a predicted value?

Sandbox Physics · 2026-10-23

Nobel contribution: 1985-1

1. Prepare a two-dimensional electron layer
2. Apply a perpendicular field
3. Measure transverse and longitudinal voltages
4. Compare plateau stability

The Hall resistance and Hall conductance are related through the full transport tensor. Longitudinal dissipation must be checked.

## The 1980 measurement used a silicon inversion layer

von Klitzing, Dorda and Pepper measured a two-dimensional electron system formed in a silicon transistor structure. In a strong perpendicular magnetic field, Hall resistance settled onto reproducible plateaus as carrier concentration changed.

The plateau values were insensitive to device geometry under the appropriate conditions. The 1985 award recognized the discovery, which gave electrical metrology a new quantum reference.

Sources: [2] [1]

## A plateau requires a transport state

In an ideal integer plateau with negligible longitudinal response, the Hall conductance is an integer multiple of the conductance quantum. Landau quantization supplies levels, and localization helps produce finite intervals between transitions. A level diagram alone is not the complete transport measurement.

$$
\begin{gathered}\sigma_{xy}=\nu\frac{e^2}{h}\\ R_{xy}=\frac{h}{\nu e^2}\quad(\rho_{xx}\rightarrow0)\end{gathered}
$$

Sources: [1] [3]

## Several checks make a useful standard

Temperature, current, contact quality and longitudinal voltage can reveal departure from the quantized state. Reproducibility across devices matters because a standard must survive changes that should not alter the invariant. Breakdown at high current is part of the operating boundary.

Sources: [1]

## Integer band models keep their own scope

The magnetic-edge and Chern-insulator Labs explain levels, boundaries and integer topology in controlled single-particle models. They are reused here. Fractional Hall liquids require correlations and are treated in a separate evidence article, not inferred from an integer Chern number.

Sources: [2] [1] [4]

Continue with the physics

## Try the related models

### [Magnetic edge spectra](https://sandboxphysics.com/labs/magnetic-edge-spectroscopy/)

Compare bulk bands and edge states in a magnetic lattice.

A single-particle magnetic lattice does not simulate a correlated fractional Hall liquid.

### [Chern insulator](https://sandboxphysics.com/labs/chern-insulator/)

Change a band mass and inspect the gap and topological response.

The band model explains an integer invariant; it has no fractional Hall quasiparticles.

## Sources and reading notes

1. [von Klitzing: The quantized Hall effect (1985)](https://www.nobelprize.org/uploads/2018/06/klitzing-lecture.pdf)

   The experimental plateau and longitudinal response require a two-dimensional electron system and controlled transport.

2. [von Klitzing, Dorda and Pepper: Quantized Hall resistance (1980)](https://doi.org/10.1103/PhysRevLett.45.494)

   Original silicon inversion-layer transport measurement.

3. [Thouless, Kohmoto, Nightingale and den Nijs: Quantized Hall conductance in a two-dimensional periodic potential (1982)](https://doi.org/10.1103/PhysRevLett.49.405)

   The original four-author calculation connects an insulating gap with integer Hall conductance.

4. [Nobel Prize in Physics 1985: official award](https://www.nobelprize.org/prizes/physics/1985/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

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