The Faraday effect revisited: General theory

Details The Faraday effect revisited: General theory The Faraday effect revisited: General theory

2005-06-17

arxiv.org/abs/cond-mat/0506428v3

J.Math.Phys.47:013511,2006

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Final version, accepted for publication in J. Math. Phys

Scientific paper

10.1063/1.2162148

This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. At zero temperature and zero frequency, if the Fermi energy lies in a spectral gap, we rigorously prove the Widom-Streda formula. For free electrons, the transverse conductivity can be explicitly computed and coincides with the classical result. In the general case, using magnetic perturbation theory, the conductivity tensor is expanded in powers of the strength of the magnetic field $B$. Then the linear term in $B$ of this expansion is written down in terms of the zero magnetic field Green function and the zero field current operator. In the periodic case, the linear term in $B$ of the conductivity tensor is expressed in terms of zero magnetic field Bloch functions and energies. No derivatives with respect to the quasi-momentum appear and thereby all ambiguities are removed, in contrast to earlier work.

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