Shubnikov–de Haas effect

An oscillation in the conductivity of a material that occurs at low temperatures in the presence of very intense magnetic fields, the Shubnikov–de Haas effect (ShdH) is a macroscopic manifestation of the inherent quantum mechanical nature of matter. It is often used to determine the effective mass of charge carriers (electrons and electron holes), allowing investigators to distinguish among majority and minority carrier populations.

Physical process

At sufficiently low temperatures and high magnetic fields, the free electrons in the conduction band of a metal, semimetal, or narrow band gap semiconductor will behave like simple harmonic oscillators. When the magnetic field strength is changed, the oscillation period of the simple harmonic oscillators changes proportionally. The resulting energy spectrum is made up of Landau levels separated by the cyclotron energy. These Landau levels are further split by the Zeeman energy. In each Landau level the cyclotron and Zeeman energies and the number of electron states (eB/h) all increase linearly with increasing magnetic field. Thus, as the magnetic field increases, the spin-split Landau levels move to higher energy. As each energy level passes through the Fermi energy, it depopulates as the electrons become free to flow as current. This causes the material's transport and thermodynamic properties to oscillate periodically, producing a measurable oscillation in the material's conductivity. Since the transition across the Fermi 'edge' spans a small range of energies, the waveform is square rather than sinusoidal, with the shape becoming ever more square as the temperature is lowered.

Related physical process

The effect is related to the de Haas–van Alphen effect, which is the name given to the corresponding oscillations in magnetization. The signature of each effect is a periodic waveform when plotted as a function of inverse magnetic field. The "frequency" of the magnetoresistance oscillations indicate areas of the extremal Fermi surface. The area of the Fermi surface is expressed in teslas.

The effect is named after Wander Johannes de Haas and Lev Shubnikov.

External links

• The article uses text from Shubnikov effect on Lang.gov that is a Public Domain as a work of a US government agency.
• Material behavior in strong magnetic fields

References

• Schubnikov, L.W.; de Haas, W.J. (1930). Proceedings of the Royal Netherlands Academy of Arts and Science 33: 130. 
• Schubnikov, L.W.; de Haas, W.J. (1930). Proceedings of the Royal Netherlands Academy of Arts and Science 33: 163.