Quantum Hall effect

The Quantum Hall effect (QHE) refers to the quantization of the Hall resistance, which may be observed in the presence of large magnetic field strength and low temperature. It was discovered in 1980 by Klaus von Klitzing, Michael Pepper, and Gerhard Dorda.

In a typical QHE experiment, a MOSFET is subjected to a large magnetic field of order 15 T, at a temperature of order 1 K. There is a two-dimensional electron gas maintained in the inversion layer of the MOSFET, the plane of which is aligned perpendicular to the magnetic field. When an electric field is applied in the plane, the corresponding Hall resistance is found to be quantized in units of

R_H = h / (e² n)

where h is Planck's constant, e the elementary charge, and n an integer. This is referred to as the Integer Quantum Hall Effect (IQHE).

In 1982, Daniel Tsui and Horst Stormer discovered the Fractional Quantum Hall Effect. Working at lower temperatures and stronger magnetic fields, they found a Hall resistance quantized in units of 3h / e², i.e. n = 1/3. Other fractional quantizations - for example, 2/5, 3/5, and 2/7 - were subsequently found. The FQHE was explained in 1983 by Robert Laughlin, using a many-body wavefunction that has a lower energy than the single-particle energy.

---

References

• K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
• D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)
• R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).