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cometzir
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Several papers (eg. Di Xiao, et. al, Berry phase effects on electronic properties, RevModPhys, 82,2010)mentioned a formula to calculate the Hall conductivity(See the picture).This formula is used in an two dimensional system, v1 and v2 are velocity operators in x and y direction, Phi0 and PhiN are ground and excited state vector.
The papers claim that this formula can be derived from the Kubo identity, but I am not sure how this can be done, since the form of Kubo formla is quite different from this expression.
Could anyone help me with the derivation?
The papers claim that this formula can be derived from the Kubo identity, but I am not sure how this can be done, since the form of Kubo formla is quite different from this expression.
Could anyone help me with the derivation?
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