Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-06-20
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
13 pages, 5 figures
Scientific paper
In the quantum Hall effect (QHE) the differential resistivity $r_{xx} \equiv r$ vanishes within a range where the Hall resistivity forms a plateau. A microscopic theory is developed, starting with a crystal lattice, setting up a BCS-like Hamiltonian in terms of composite bosons, and using statistical mechanical method. The main advantage of our bosonic theory is its capability of explaning the plateau formation in the Hall resistivity, which is assumed in the composite fermion theories. In the QHE under radiation, the resistivity vanishes within a range with no plateau formation. This is shown in terms of two-channels model, one channel excited by radiation where the supercurrents run and the other (base) channel in which the normal currents run. The transport diamonds (TD) and the zero direct current anomaly (ZCA) occur when the resistivity $r$ is measured as a function of magnetic field and direct current (DC). The spiral motion of an electron under a magnetic field can be decomposed into two, the cyclotron motion with the cyclotron mass $m^*$ and the guiding center motion with the magnetotransport $M^*$. The quantization of the motion generates magnetic oscillations in the density of states. The magnetoconductivity is calculated, using kinetic theory and quantum statistical mechanics. The TR and ZCA are shown to be a breakdown of QHE. The integer QHE minima are shown to become the Shubnikov-de Haas (SdH) maxima progressively as the DC increases. The ZCA at low temperatures ($T=0.253$--1.2\,K) is temperature-dependent, which is caused by the electron-optical-phonon scattering.
Fujita Shigeo
Ho Hsin-Cheng
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