Semiclassical theories of the anomalous Hall effect

@article{Sinitsyn2007SemiclassicalTO,
  title={Semiclassical theories of the anomalous Hall effect},
  author={Nikolai A. Sinitsyn},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2007}
}
  • N. Sinitsyn
  • Published 2 December 2007
  • Physics
  • arXiv: Mesoscale and Nanoscale Physics
Recently, the semiclassical theory of the anomalous Hall effect induced by the Berry curvature in Bloch bands has been introduced. The theory operates only with gauge invariant concepts, that have a simple semiclassical interpretation and provides a clear distinction among various contributions to the Hall current. While the construction of such an approach to the anomalous Hall effect problem has been long sought, only the new semiclassical theory demonstrated the agreement with quantitative… 

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References

SHOWING 1-10 OF 166 REFERENCES
A simple theory of the anomalous hall effect in semiconductors
The anomalous Hall effect in a two band semiconductor is treated by an elementary theory based on the use of an effective Hamiltonian in the conduction band. Simple equations of motion for the
Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
Electrons in a crystal generically experience an anomalous coordinate shift (a side jump) when they scatter off a defect. We propose a gauge invariant expression for the side jump associated with
Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach
The anomalous Hall effect AHE is a consequence of spin-orbit coupling in a ferromagnetic metal and related primarily to density-matrix response to an electric field that is off-diagonal in band
Contribution to the theory of the anomalous Hall effect: Influence of the band structure on the skew scattering
The use of wavefunctions which properly include the periodic part of the spin-orbit interaction, allows one to show that the matrix elements of a scattering potential contain an asymmetric part. When
Anomalous Hall effect in a two-dimensional electron gas
The anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling is studied within the Kubo-Streda formalism in the presence of pointlike potential impurities. We
Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation
A model to treat the anomalous Hall effect is developed. Based on the Kubo formalism and on the Dirac equation, this model allows the simultaneous calculation of the skew-scattering and side-jump
Anomalous Hall effect in paramagnetic two-dimensional systems
We investigate the possibility of observing the anomalous Hall effect in paramagnetic two-dimensional systems. We apply the semiclassical equations of motion to carriers in the conduction and valence
Anomalous Hall Effect —A New Perspective—
Recent developments on the studies of the anomalous Hall effect are reviewed from the quantum geometrical viewpoint. Accumulating evidences show that the intrinsic contribution due to the Berry phase
Intrinsic versus extrinsic anomalous Hall effect in ferromagnets.
TLDR
A unified theory of the anomalous Hall effect (AHE) is presented for multiband ferromagnetic metals with dilute impurities, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit coupling.
Localization corrections to the anomalous Hall effect in a ferromagnet
We calculate the localization corrections to the anomalous Hall conductivity related to the contribution of spin-orbit scattering into the current vertex ~side-jump mechanism!. We show that in
...
1
2
3
4
5
...