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Title: Diagrammatic approach to nonlinear optical response with application to Weyl semimetals

Nonlinear optical responses are a crucial probe of physical systems including periodic solids. In the absence of electron-electron interactions, they are calculable with standard perturbation theory starting from the band structure of Bloch electrons, but the resulting formulas are often large and unwieldy, involving many energy denominators from intermediate states. This work gives a Feynman diagram approach to calculating nonlinear responses. This diagrammatic method is a systematic way to perform perturbation theory, which often offers shorter derivations and also provides a natural interpretation of nonlinear responses in terms of physical processes. Applying this method to second-order responses concisely reproduces formulas for the second-order-harmonic shift current. We then apply this method to third-order responses and derive formulas for third-order-harmonic generation and self-focusing of light, which can be directly applied to tight-binding models. Third-order responses in the semiclasscial regime include a Berry curvature quadrupole term, whose importance is discussed including symmetry considerations and when the Berry curvature quadrupole becomes the leading contribution. In conclusion, the method is applied to compute third-order optical responses for a model Weyl semimetal, where we find a new topological contribution that diverges in a clean material, as well as resonances with a peculiar linear character.
Authors:
ORCiD logo [1] ;  [2] ;  [2] ;  [2]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Physics
  2. Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
Publication Date:
Grant/Contract Number:
AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 4; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
Univ. of California, Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Nonlinear optics; conductivities
OSTI Identifier:
1490189
Alternate Identifier(s):
OSTI ID: 1490517

Parker, Daniel E., Morimoto, Takahiro, Orenstein, Joseph, and Moore, Joel E.. Diagrammatic approach to nonlinear optical response with application to Weyl semimetals. United States: N. p., Web. doi:10.1103/PhysRevB.99.045121.
Parker, Daniel E., Morimoto, Takahiro, Orenstein, Joseph, & Moore, Joel E.. Diagrammatic approach to nonlinear optical response with application to Weyl semimetals. United States. doi:10.1103/PhysRevB.99.045121.
Parker, Daniel E., Morimoto, Takahiro, Orenstein, Joseph, and Moore, Joel E.. 2019. "Diagrammatic approach to nonlinear optical response with application to Weyl semimetals". United States. doi:10.1103/PhysRevB.99.045121.
@article{osti_1490189,
title = {Diagrammatic approach to nonlinear optical response with application to Weyl semimetals},
author = {Parker, Daniel E. and Morimoto, Takahiro and Orenstein, Joseph and Moore, Joel E.},
abstractNote = {Nonlinear optical responses are a crucial probe of physical systems including periodic solids. In the absence of electron-electron interactions, they are calculable with standard perturbation theory starting from the band structure of Bloch electrons, but the resulting formulas are often large and unwieldy, involving many energy denominators from intermediate states. This work gives a Feynman diagram approach to calculating nonlinear responses. This diagrammatic method is a systematic way to perform perturbation theory, which often offers shorter derivations and also provides a natural interpretation of nonlinear responses in terms of physical processes. Applying this method to second-order responses concisely reproduces formulas for the second-order-harmonic shift current. We then apply this method to third-order responses and derive formulas for third-order-harmonic generation and self-focusing of light, which can be directly applied to tight-binding models. Third-order responses in the semiclasscial regime include a Berry curvature quadrupole term, whose importance is discussed including symmetry considerations and when the Berry curvature quadrupole becomes the leading contribution. In conclusion, the method is applied to compute third-order optical responses for a model Weyl semimetal, where we find a new topological contribution that diverges in a clean material, as well as resonances with a peculiar linear character.},
doi = {10.1103/PhysRevB.99.045121},
journal = {Physical Review B},
number = 4,
volume = 99,
place = {United States},
year = {2019},
month = {1}
}

Works referenced in this record:

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986

First Principles Calculation of the Shift Current Photovoltaic Effect in Ferroelectrics
journal, September 2012