TY - JOUR

T1 - Lattice polarization effects on the screened Coulomb interaction W of the GW approximation

AU - Lambrecht, Walter R.L.

AU - Bhandari, Churna

AU - Van Schilfgaarde, Mark

PY - 2017/9/19

Y1 - 2017/9/19

N2 - 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/q2 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 q→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 -αPωLO/2 of the polaron effect with αP the polaron coupling factor.

AB - 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/q2 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 q→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 -αPωLO/2 of the polaron effect with αP the polaron coupling factor.

UR - http://www.scopus.com/inward/record.url?scp=85044434810&partnerID=8YFLogxK

U2 - 10.1103/PhysRevMaterials.1.043802

DO - 10.1103/PhysRevMaterials.1.043802

M3 - Article

AN - SCOPUS:85044434810

SN - 2475-9953

VL - 1

JO - Physical Review Materials

JF - Physical Review Materials

IS - 4

M1 - 043802

ER -