method: Linear-response perturbation theory*

We have developed a new theoretical and computational method to calculate electron-phonon coupling from first principles, based on the GW method that includes quasiparticle self-energy effects. This GW perturbation theory (GWPT) applies monochromatic (fixed wavevector) phonon perturbations to the electron self-energy, using linear response theory, to calculate the electron-phonon matrix elements including many-electron effects. GWPT shares a similar spirit as density-functional perturbation theory but goes beyond the independent-particle picture. The GWPT method naturally scales linearly with the number of phonon modes, therefore largely reduces the computation costs, and increases the accuracy compared with frozen-phonon technique. We will present the general formalism, the implementation of GWPT, and apply the method to several physical systems.