Ab initio electron-phonon interactions in correlated electron systems

Electron-phonon ($e$-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons and metal-insulator transitions. First-principles approaches enable accurate calculations of $e$-ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable $e$-ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials and multiferroics. Here we show first-principles calculations of $e$-ph interactions in CES, using the framework of Hubbard-corrected density functional theory (DFT+$U$ ) and its linear response extension (DFPT+$U$), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its $e$-ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged $e$-ph interactions, DFPT+$U$ is shown to remove the divergences and properly account for the long-range Frohlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e-ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.

Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN

First-principles calculations of $e$-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) $e$-ph interaction, a long-range scattering mechanism due to acoustic phonons in non-centrosymmetric polar materials, is not accurately described at present. Current calculations include short-range $e$-ph interactions (obtained by interpolation) and the dipole-like Frohlich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the long-range $e$-ph interaction due to dynamical quadrupoles, and apply this framework to investigate $e$-ph interactions and the carrier mobility in the PE material wurtzite GaN. We show that the quadrupole contribution is essential to obtain accurate $e$-ph matrix elements for acoustic modes and to compute PE scattering. Our work resolves the outstanding problem of correctly computing $e$-ph interactions for acoustic modes from first principles, and enables studies of $e$-ph coupling and charge transport in PE materials.