Shubnikovde

Shubnikovde, short for the Shubnikov–de Haas effect, refers to quantum oscillations observed in the electrical resistivity of metals and doped semiconductors when subjected to strong magnetic fields at low temperatures. The resistivity oscillates periodically with the inverse magnetic field, 1/B, revealing details of the material’s electronic structure.

Discovered in the early 1930s by Lev M. Shubnikov and Wander de Haas, the effect was observed in metals such as copper and bismuth. It is a direct manifestation of Landau quantization of electronic motion in magnetic fields and is closely related to other quantum oscillations seen in solids.

Principle: In a magnetic field, electron motion becomes quantized into Landau levels with discrete energies. As 1/B is varied, these Landau levels move through the Fermi energy, causing the density of states at the Fermi level to oscillate. This drives periodic changes in transport properties, including resistivity. The oscillation frequency in 1/B is determined by the extremal cross-sectional area of the Fermi surface perpendicular to the field via the Onsager relation F = (ħ/2πe) A_F.

Measurement and theory: Observations require high material purity and low temperatures to reduce thermal smearing. The amplitude and damping of the oscillations are described by the Lifshitz–Kosevich formalism, which depends on the effective mass m*, temperature, and scattering (Dingle) factor. From the data, researchers can extract Fermi-surface geometry, carrier masses, and scattering rates.

Applications: The Shubnikov–de Haas effect is widely used to map Fermi surfaces and determine fundamental electronic parameters in metals, semiconductors, and low-dimensional systems, contributing to the understanding of electronic structure and transport phenomena.