Long-range quadrupole electron-phonon interaction from first principles

Abstract

Lattice vibrations in materials induce perturbations on the electron dynamics in the form of long-range (dipole and quadrupole) and short-range (octopole and higher) potentials. The dipole Fröhlich term can be included in current first-principles electron-phonon (e-ph) calculations and is present only in polar materials. The quadrupole e-ph interaction is present in both polar and nonpolar materials, but currently it cannot be computed from first principles. Here we show an approach to compute the quadrupole e-ph interaction and include it in ab initio calculations of e-ph matrix elements. The accuracy of the approach is demonstrated by comparing with direct density functional perturbation theory calculations. We apply our method to silicon as a case of a nonpolar semiconductor and tetragonal PbTiO 3 as a case of a polar piezoelectric material. In both materials we find that the quadrupole term strongly impacts the e-ph matrix elements. Analysis of e-ph interactions for different phonon modes reveals that the quadrupole term mainly affects optical modes in silicon and acoustic modes in PbTiO 3 , although the quadrupole term is needed for all modes to achieve quantitative accuracy. The effect of the quadrupole e-ph interaction on electron scattering processes and transport is shown to be important. Our approach enables accurate studies of e-ph interactions in broad classes of nonpolar, polar, and piezoelectric materials.

Phonon-limited electron mobility in Si, GaAs, and GaP with exact treatment of dynamical quadrupoles

“…Note added. Recently, we became aware of a related work by another group that reaches similar conclusions about the importance of the dynamical quadrupole term to obtain an accurate physical description of e-ph interactions [89,90]. = e ik•S −1 (r+R−f ) u nk (S −1 (r − f )) = e i t S −1 k•R ψ nk (S −1 (r − f )) = e i Sk•RŜ f ψ nk (r),…”

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

“…Our analysis highlights the large errors resulting from including only the Fröhlich term in GaN [29], which greatly overestimates the acoustic mode e-ph interactions [29,30]. Our companion paper [31] applies this framework to silicon and the PE material PbTiO 3 . The quadrupole e-ph interaction, which critically corrects the dipole term in polar materials, is sizable in nonpolar materials, where it is the leading long-range e-ph interaction, and it is essential to correctly compute the e-ph matrix elements.…”

“…We derive the first-principles quadrupole e-ph interaction g quad mnν ðk; qÞ by superimposing two oppositely oriented dipole moments, as discussed in detail in our companion paper [31], and obtain:…”

Remote free-carrier screening to boost the mobility of Fröhlich-limited two-dimensional semiconductors

“…Details of this model, as well as a comparison with direct DFPT calculations are given in Appendix A 3. Only first-order dipole potentials are considered, quadrupole contributions [52][53][54][55] are neglected. In principle, multilayer materials generate several polar-optical phonons with different phase shifts in the layers [45,56].…”