Abstract
A loop diagram approach to the nonlinear optical conductivity of an electron-phonon system is introduced. This approach can be categorized as another Feynman-like scheme because all contributions to the self-energy terms can be grouped into topologically-distinct loop diagrams. The results for up to the first order nonlinear conductivity are identical to those derived using the KC reduction identity (KCRI) and the state- dependent projection operator (SDPO) introduced by the present authors. The result satisfies the “population criterion” in that the population of electrons and phonons appear independently or the Fermi distributions are multiplied by the Planck distributions in the formalism. Therefore it is possible, in an organized manner, to present the phonon emissions and absorptions as well as photon absorptions in all electron transition processes. In additions, the calculation needed to obtain the line shape function appearing in the energy denominator of the conductivity can be reduced using this diagram method. This method shall be called the “KC loop diagram method”, since it originates from proper application of KCRI’s and SDPO’s.
Highlights
Studies of the optical transitions in electron systems are powerful for examining the electronic structure of solids, because the absorption lineshapes are quite sensitive to the type of scattering mechanism affecting the transport of electrons and to the interaction of electrons with intense laser light
A loop diagram approach to the nonlinear optical conductivity of an electron-phonon system is introduced. This approach can be categorized as another Feynman-like scheme because all contributions to the self-energy terms can be grouped into topologically-distinct loop diagrams
The results for up to the first order nonlinear conductivity are identical to those derived using the KC reduction identity (KCRI) and the statedependent projection operator (SDPO) introduced by the present authors
Summary
Studies of the optical transitions in electron systems are powerful for examining the electronic structure of solids, because the absorption lineshapes are quite sensitive to the type of scattering mechanism affecting the transport of electrons and to the interaction of electrons with intense laser light. The lattice distortion in turn has a feedback on the electron dynamics, resulting in an increase in the electron mass and a shortening of the electron lifetime in a particular quasi-particle state. This effect is described in terms of the self-energy that the electron acquires due to the electron-phonon interaction. This paper introduces a method for the nonlinear optical conductivity and line shape functions to represent them in loop diagrams It can be categorized as another Feynman-like scheme because all the contributions to the line shape functions (or self-energy terms) can be grouped into topologicallydistinct diagrams. The diagram approach to the nonlinear phenomena is based on the following methods
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