The electron–phonon renormalization in the electronic structure calculation: Fundamentals, current status, and challenges

Electron-phonon (e-ph) interaction plays a crucial role in determining many physical properties of the materials, such as the superconducting transition temperature, the relaxation time and mean free path of hot carriers, the temperature dependence of the electronic structure, and the formation of the vibrational polaritons. In the past two decades, the calculations of e-ph properties from first-principles has become possible. In particular, the renormalization of electronic structures due to e-ph interaction can be evaluated, providing greater insight into the quantum zero-point motion effect and the temperature dependence behavior. In this perspective, we briefly overview the basic theory, outline the computational challenges, and describe the recent progress in this field, as well as future directions and opportunities of the e-ph coupling calculations.