Pseudospin Quantum Hall Ferromagnetism

Symmetry breaking ground states occur in quantum Hall effect (QHE) systems when two or more Landau levels become degenerate near the Fermi level. Isotropic, easy-axis or easy plane quantum Hall ferromagnets (QHF) can form depending on the pseudospins of the involved Landau levels consisting of real spin, orbit radius quantum number, subband index or growth direction. Theories based on Hartree-Fock calculation of pseudospin anisotropy energy are introduced, which classify the type of QHFs according to the nature of the degenerate Landau levels. Several representative experimental studies on the emergence of integer QHF in single-layer and doublelayer two dimensional electron systems as well as of fractional QHF are presented. The anisotropy types are identified from the experimental measurements and compared with the prediction from the Hartree-Fock calculation. Discrepancy arises when neglected factors in the simple theoretical model become significant such as charge distribution profiles of different subbands, orbital effect of the in-plane magnetic field, softness of the barrier etc.