The quantum Hall effect is a resistance standard. Its quantized Hall conductance, expressed in units of the von Klitzing constant, provides the most precise resistance measurement in metrology. This is what the quantum Hall effect is for, in the minds of most physicists. A calibration tool.

In Corbino disk geometry, it becomes a refrigerator.

The Peltier effect — thermoelectric cooling where current flow carries heat from one junction to another — exists in every conductor. In most materials it is weak, barely measurable against Joule heating. In the quantum Hall regime, Landau level quantization concentrates the Peltier coefficient into sharp, controllable windows that alternate between heating and cooling as the magnetic field sweeps through filling factors.

In the Corbino geometry — a disk with contacts at the inner and outer radii — the current flows radially while the Hall voltage drives circumferential drift. This geometry separates the Peltier cooling from the bulk Joule heating more cleanly than Hall bar geometries. The outer edge can be cooled below the bath temperature. Net cooling. Not reduced heating — actual refrigeration.

The Peltier coefficient approaches a predictable saw-tooth pattern in the clean limit, with sharp peaks at filling factor transitions. The peaks occur where the chemical potential passes through a Landau level — exactly where the system's ability to carry entropy per unit charge changes discontinuously. The quantized structure that makes the quantum Hall effect a good resistance standard also makes it a controllable heat pump.

This is not a repurposing of the quantum Hall effect. The Peltier cooling and the quantized resistance arise from the same underlying physics: the quantized structure of electronic states in a magnetic field. The same quantization that pins the Hall conductance to integer multiples of e²/h also pins the Peltier coefficient to predictable values at each filling factor. The metrology application and the refrigeration application are the same phenomenon, observed in different thermodynamic quantities.

The quantum Hall effect was always a heat engine. We measured the wrong output.