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Carriers in Magnetic Fields and Temperature Gradients

  • Karl W. Böer
  • Udo W. PohlEmail author
Living reference work entry

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Abstract

The application of a magnetic field in addition to an electric field yields significant information on carrier polarity and mobility, on the effective mass, and on the origin of energy levels in paramagnetic centers. If a temperature gradient exists in addition to an electric field, thermoelectric effects occur with useful applications, such as the Seebeck effect rendering thermoelectricity used in thermocouples and the Peltier effect applied for cooling. If a magnetic field is added to the temperature gradient and to the electric field, several galvanomagnetic and thermomagnetic effects are observed.

In strong magnetic fields, the electronic density of states is changed: energy levels condense on quantized Landau levels with cylindrical equi-energy surfaces in k space. Quantities controlled by their vicinity to the Fermi energy then show an oscillatory dependence on the magnetic field, such as the DeHaas-van Alphen oscillations of the magnetic susceptibility and Shubnikov-DeHaas oscillations of the resistivity.

If scattering is suppressed in highly pure samples at very low temperature, a strong magnetic field forces carriers to propagate on edge states at the sample surface, creating a topological insulator with no conductance in the bulk. In a two-dimensional electron gas, this leads to the quantum Hall effect, which established an international metrological standard for the electrical resistance. The related fractional quantum Hall effect lead to the discovery of composite fermions, quasi-particles composed of an electron and flux quanta, which conjointly carry a fractional charge. The quantum spin Hall phase represents a third type of topological insulators, which require no external magnetic field.

Keywords

DeHaas-van Alphen effect Fractional quantum Hall effect Galvanomagnetic effects Hall effect Hall mobility Landau levels Magnetoresistance Peltier effect Quantum Hall effect Quantum spin Hall phase Seebeck effect Shubnikov-DeHaas effect Thermoelectric effects Thermomagnetic effects Topological insulator 

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Copyright information

© Springer International Publishing AG 2020

Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Institut für Festkörperphysik, EW5-1Technische Universität BerlinBerlinGermany

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