# 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. In this work, we adopt a simple estimate forthe 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 radiusfrom the inverse of the polaron length scale. The gap correction is shown to agree with Fröhlich’s simple estimate -α _{P}ω _{LO}/2 of the polaron effect with α _{P} the polaron coupling factor.

- Authors:

- Case Western Reserve Univ., Cleveland, OH (United States)
- Univ. of Missouri, Columbia, MO (United States)
- King's College London (United Kingdom)

- Publication Date:

- Research Org.:
- Case Western Reserve Univ., Cleveland, OH (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1591868

- Alternate Identifier(s):
- OSTI ID: 1392716

- Grant/Contract Number:
- [SC0008933]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Materials

- Additional Journal Information:
- [ Journal Volume: 1; Journal Issue: 4]; Journal ID: ISSN 2475-9953

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Lambrecht, Walter R. L., Bhandari, Churna, and van Schilfgaarde, Mark. Lattice polarization effects on the screened Coulomb interaction W of the GW approximation. United States: N. p., 2017.
Web. doi:10.1103/PhysRevMaterials.1.043802.
```

```
Lambrecht, Walter R. L., Bhandari, Churna, & van Schilfgaarde, Mark. Lattice polarization effects on the screened Coulomb interaction W of the GW approximation. United States. doi:10.1103/PhysRevMaterials.1.043802.
```

```
Lambrecht, Walter R. L., Bhandari, Churna, and van Schilfgaarde, Mark. Tue .
"Lattice polarization effects on the screened Coulomb interaction W of the GW approximation". United States. doi:10.1103/PhysRevMaterials.1.043802. https://www.osti.gov/servlets/purl/1591868.
```

```
@article{osti_1591868,
```

title = {Lattice polarization effects on the screened Coulomb interaction W of the GW approximation},

author = {Lambrecht, Walter R. L. and Bhandari, Churna and van Schilfgaarde, Mark},

abstractNote = {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. In this work, we adopt a simple estimate forthe 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 radiusfrom 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.},

doi = {10.1103/PhysRevMaterials.1.043802},

journal = {Physical Review Materials},

number = [4],

volume = [1],

place = {United States},

year = {2017},

month = {9}

}

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