Electron-phonon (e-ph) interactions play an important role in condensed matter, since they inu- ence the properties and lifetimes of both the electron and the phonon quasi-particles. In addition, tuning e-ph offers great promise for material design at the nanoscale . Although _rst-principles study of e-ph has been made for simple, prototypical materials over the last decade [2,3,4,5], ap- plying these methods for large and complex systems is challenging.
In this talk, we will present the diverse strategies that we have pursued in recent years to over- come these limitations. First, we will present our real-space implementation of density-functional perturbation theory (DFPT) in the all-electron, numeric atomic orbitals based code FHI-aims , which enables us to study large and complex systems due to the computational efficiency of local- ized basis sets. Second, we will discuss how we systematically studied the e-ph in real material, such as ZnO, TiO2 and 82 binary materials in both the rocksalt (RS) and the zincblende (ZB) structure. We have extended the existing _nite-difference schemes such as phonopy  to inves- tigate the small/large polaron by using the hybrid functional . Eventually, we will critically review the individual advantages and limitations of these techniques, discuss ongoing development efforts, and showcase possible future applications.
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