Ab initio calculation of nonlinear optical properties for chiral carbon nanotubes. Second harmonic generation and dc-Pockels effect

  • Michel Rérat
  • Panaghiotis Karamanis
  • Bartolomeo Civalleri
  • Lorenzo Maschio
  • Valentina Lacivita
  • Bernard Kirtman
Regular Article
  • 78 Downloads
Part of the following topical collections:
  1. In Memoriam of Claudio Zicovich

Abstract

Although the static first hyperpolarizability \(\beta\) of graphene and chiral carbon nanotubes (CNTs) vanishes by symmetry, that is no longer true for frequency-dependent fields in which case there is a unique nonzero component. We evaluate that component for the dc-Pockels effect and second harmonic generation of several CNTs by means of the coupled perturbed Kohn–Sham method with the CAM-B3LYP functional as implemented in the CRYSTAL code. Both electronic and vibrational contributions are considered. Of particular interest is the frequency dependence in the region below the first resonance. Our results for the role of band gap, type of chirality, CNT radius and effect of orbital relaxation are analyzed using the conventional sum-over-states formulation in conjunction with the calculated band structure and density of states.

Keywords

Chiral carbon nanotubes dc-Pockels effect Second harmonic generation Coupled perturbed Kohn–Sham method CRYSTAL code 

Notes

Acknowledgements

This work would not have been possible without the invaluable contribution given by our colleague and friend Claudio M. Zicovich-Wilson to the exploitation of symmetry in periodic systems, starting from his two seminal papers on symmetry-adapted crystalline orbitals [47, 48] to the use of symmetry for large crystalline solids, nanotubes, helices and fullerenes. Yet, his work was of great relevance to dramatically reduce the computational cost in the CRYSTAL code (i.e., one and two-electron integrals, SCF process, and many other properties).

Supplementary material

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Supplementary material 1 (pdf 0 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IPREMCNRS / Université de Pau et des Pays de l’Adour, UMR5254PauFrance
  2. 2.Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) CentreUniversità di TorinoTorinoItaly
  3. 3.Materials Sciences DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  4. 4.Department of Chemistry and BiochemistryUniversity of CaliforniaSanta BarbaraUSA

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