Itinerant Spin Dynamics in Structures of ... - Jacobs University

Chapter 5: Spin Hall Effect 103
Comparing directly the integrand of Eq.(5.55) with Eq.(5.53) it follows that the moments
of the expansion of the imaginary part of the correlation function are given by
∫ 1 D−1
∑
µ n = − d˜ω 〈0|A|k〉〈k|B|0〉δ(˜ω −Ẽk) T n (˜ω) (5.57)
−1
k=0
} {{ }
=
≡j(˜ω)
〈
∣
0∣AT n (− ˜H)B
〉
∣
∣0 . (5.58)
Finally the reconstruction is done by using Eq.(5.32).
This scheme has to be adapted to calculate the SHC σ SH in a finite system, as presented
in Eq.(5.22),
σ SH (E F ) = 2 e V
∑
E m