Berry phase and Hall effect in magnets and semiconductors

Berry phase and Hall effect in magnets and semiconductors
Naoto Nagaosa
CREST, Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
It has been recently recognized that the Berry phase curvature of the Bloch wavefunctions in the momentum space leads to the Hall current perpendicular to the applied electric field. This current is driven
by the anomalous velocity due to the Berry phase, quite distict from the usual transport current which is
produced by the shift of the electron distribution function. Therefore all the occupied states contribute
to this equlibrium dissipationless Hall current, which is analogous to the superconducting current and
quantum Hall current. I will talk on the two realizations of this Hall current in solids, i.e, the anomalous
Hall current in ferromagnets and the spin Hall current in semiconductors. In addition to the fundamental
physics governing to this phenomena, many factors relevant to realistic systems such as the impurity
scattering and contact to the electrodes are discussed. Various recent experiments are also discussed.
Sorting category: Dd Conducting electrons in condensed matter
Keywords: Berry phase, anomalous Hall effect, spin Hall effect