Projection-Reduction Approach to Optical Conductivities for an Electron-Phonon System and Their Diagram Representation

Figure 9

Schematic diagrams of (a) |𝐶_𝜆𝛼(𝑞)|²𝐺_𝛾⁽⁻⁾_1𝜆(𝜔₁₂)[𝑃₊(𝛾₁,𝜆)−𝑃₊(𝛾₂,𝜆)], (b) |𝐶_𝜆𝛼(𝑞)|²𝐺_𝛾⁽⁺⁾_1𝜆(𝜔₁₂)[𝑃₋(𝛾₁,𝜆)−𝑃₋(𝛾₂,𝜆)], (c) |𝐶_𝛽𝜆(𝑞)|²𝐺⁽⁻⁾_𝜆𝛼(𝜔₁₂₃) [𝑃₊(𝜆,𝛾₂)−𝑃₊(𝜆,𝛾₁)], and (d) |𝐶_𝛽𝜆(𝑞)|²𝐺⁽⁺⁾_𝜆𝛼(𝜔₁₂₃) [𝑃₋(𝜆,𝛾₂)−𝑃₋(𝜆,𝛾₁)] in Γ⁽²³⁾_{𝛽𝛾1𝛾2𝛼}(𝜔₁,𝜔₂,𝜔₃).

(a)

(b)

(c)

(d)