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 noncentrosymmetric polar materials, is not accurately described at present. Current calculations include short-range e-ph interactions (obtained by interpolation) and the dipolelike Frolich 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 quadrupolcs, 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.