Lattice polarization effects on the screened Coulomb interaction $W$ of the GW approximation

Abstract

In polar insulators where longitudinal and transverse optical phonon modes differ substantially, the electron-phonon coupling affects the energy-band structure primarily through the long-range Fröhlich contribution to the Fan term. This diagram has the same structure as the $GW$ self-energy where $W$ originates from the electron part of the screened coulomb interaction. The two can be conveniently combined by combining electron and lattice contributions to the polarizability. Both contributions are nonanalytic at the origin, and diverge as $1/q^2$ so that the predominant contribution comes from a small region around $q=0$. Here we adopt a simple estimate for the Fröhlich contribution by assuming that the entire phonon part can be attributed to a small volume of $q$ near $q=0$. We estimate the magnitude for $\mathbf{q}\to 0$ from a generalized Lyddane-Sachs-Teller relation, and the radius from the inverse of the polaron length scale. The gap correction is shown to agree with Fröhlich's simple estimate $-{\alpha }_P{\omega }_L/2$ of the polaron effect.

References in corpus (16)

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• Dielectric anisotropy in the GW space-time method
• Quasiparticle self-consistent GW method based on the augmented plane-wave and muffin-tin orbital method
• Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors. Results for zincblende GaN
• Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method

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• All-electron quasi-particle self-consistent $GW$ band structures for SrTiO${}_3$ including lattice polarization corrections in different phase
• Ultrathin 2D-oxides: a perspective on fabrication, structure, defect, transport, electron and phonon properties
• Remarkable band gap renormalization via dimensionality of the layered material C3B
• Quasiparticle self-consistent $GW$ band structures and high-pressure phase transitions of LiGaO${}_2$ and NaGaO$_2
• Temperature effects in topological insulators of transition metal dichalcogenide monolayers
• All-electron Quasiparticle Self-consistent GW for Molecules and Periodic Systems within the Numerical Atomic Orbital Framework