Schubnikow-de-Haas effect

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Lev Shubnikov

In solid-state physics, the Schubnikow-de-Haas effect describes the oscillation of the electrical resistance of a pure single crystal as a function of a strong external magnetic field at low temperatures . The effect named after Lew Wassiljewitsch Schubnikow and Wander Johannes de Haas is based on the same physical principles as the De Haas van Alphen effect . In contrast, the also be resettled in this field describes the quantum Hall effect a perpendicular to a current flow forming electrical voltage .

The oscillations in the resistance with an externally applied magnetic field were first discovered in 1930 on bismuth by the two namesake. These results supported the predictions for the quantization of the energy states in the magnetic field in so-called Landau levels through experimental results.

At low temperatures and strong magnetic fields, the free electrons behave like quantum mechanical harmonic oscillators , that is, their energy levels perpendicular to the magnetic field are quantized ( Landau level ). When the magnetic field becomes stronger, the distance between these levels increases, their position shifts relative to the Fermi energy . If the Fermi energy lies within a Landau level - broadened into a band by electron-phonon collisions - the electrons can scatter and the electrical resistance changes depending on the magnetic field. It becomes maximum when the Fermi energy is in the middle of the level, since the ratio of conduction electrons to free states that can be reached by scattering then just becomes one. If the Fermi energy lies between two Landau levels, the electrons cannot overcome the energy gap to the next level due to the low temperature, scattering is no longer possible and the resistance drops. A clear explanation is given in the context of the marginal channel model .

The Schubnikow-de-Haas effect is used (in part similar to the quantum Hall effect ) to be able to determine certain material properties. These include u. A .:

  • Determination of the Fermi area ;
  • Determination of the charge carrier density (from the oscillation frequency);
  • Characterization of highly doped , inhomogeneous structures (several frequencies occur);
  • Determination of the effective mass of the charge carriers (measurement at two different temperatures);
  • Characterization of superlattice semiconductor structures.

literature

  • Harald Ibach, Hans Lüth: Solid State Physics . Springer, ISBN 3-540-66074-7 .
  • Supriyo Datta: Electronic Transport in Mesoscopic Systems . Cambridge University Press, ISBN 0-521-41604-3 .
  • L. Schubnikow, WJ de Haas: Magnetic Resistance Increase in Single Crystals of Bismuth at Low Temperatures . In: Proceedings of the Koninklijke Akademie Van Wetenschappen Te Amsterdam . tape 33 , 1930, pp. 130 .

credentials

  1. ^ L. Schubnikow, WJ De Haas: A New Phenomenon in the Change of Resistance in a Magnetic Field of Single Crystals of Bismuth. In: Nature . tape 126 , no. 3179 , October 4, 1930, p. 500 , doi : 10.1038 / 126500a0 .
  2. ↑ L. Landau: Diamagnetism of Metals . In: Journal of Physics . tape 64 , no. 9-10 , September 1930, pp. 629-637 , doi : 10.1007 / BF01397213 .