Figure 5

Diagram for the calculation of the conductivity. Diagram for the calculation of the conductivity (to the leading order) of an array of 2LA with the radiation emitted and absorbed by another parallel array which has an external source of electron with frequency \({\omega }_{e}\). The frequency is conserved, but the momentum satisfies only crystal momentum conservation. Each dotted line represents an insertion of momentum k from the current operator. The double-line (single-line) is the renormalized propagator of the upper field (lower field) \({\tilde{\Delta }}_{\alpha }^{(1)\pm }(k,\omega )\) (Eq. 16), and wavy-line represents the renormalized photonic propagator \(\tilde{G}(k,\omega ^{\prime} ;k^{\prime} ,\omega ^{\prime} )\) (Eq. 17).