Electron-phonon coupling is ubiquitous in condensed matter, from superconductivity to thermal and electronic transport. First-principles calculations of electron-phonon coupling have almost exclusively been based on semilocal density functional theory, but recent work has shown that electronic correlation can significantly modify the strength of electron-phonon coupling in a range of materials. Unfortunately, the computational expense of going beyond semilocal density functional theory places severe limits to the calculation of electron-phonon coupling in this regime.

In this talk, I will present some recent developments that significantly reduce the computational expense of the calculation of electron-phonon coupling using finite differences [1,2]. Using these methods, it becomes feasible to include effects such as electronic correlation or the spin-orbit interaction in the calculation of electron-phonon coupling. I will describe some applications, such as the effects of using the GW approximation to calculate the temperature dependence of the band structure of standard semiconductors [3] and the prediction of temperature-induced topological phase transitions in topological insulators [4].

[1] Lloyd-Williams and Monserrat, Phys. Rev. B 92, 184301 (2015)

[2] Monserrat, Phys. Rev. B 93, 014302 (2016)

[3] Monserrat, Phys. Rev. B 93, 100301(R) (2016)

[4] Monserrat and Vanderbilt, arXiv:1608.00584 [cond-mat.mtrl-sci]