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Non-linear response of low dimensional structures
C. Attaccalite1, A. Naguer1, E. Cannuccia1, M. Grüning2
1) Université Grenoble Alpes, Institut Nèel, CNRS, Grenoble (France) claudio.attaccalite@grenoble.cnrs.fr
2) School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland, UK
Theory: a real-time approach to study non-linear response functions
Second Harmonic Generation (SHG) in 2D crystals
Third-Harmonic Generation in nanotubes and nanoribbons
Conclusions
We present an ab-initio study of non-linear response of low dimensional structures. In particular we investigate second-harmonic generation (SHG) in two dimensional crystals, MoS2, h-BN, ZnO, GaN and SiC, and third-harmonic-generation (THG) in carbon nanotubes and nanoribbons. The non-linear response functions are obtained from a real-time approach based on dynamical Berry phase to threat the coupling between the external field and electrons.
We start from the Kohn-Sham eigenvectors and eigenvalues plus an external electric field
We propagate in real-time a Schroedinger like equation where correlation effects are included as a single particle operators in H0k
Polarization is calculated in terms of dynamical Berry-Phase
Phys. Rev. B 88, 235113(2013)
Fourier analysis is used to extract all the response functions c(1),c(2)...
Correlation effects are larger in low dimensional systems. In this example we show the SHG of an
h-BN monolayer. Bound excitons are clearly visible in the linear and non-linear response
PRB 89, 081102(R) (2014)
GW + BSE
c(2)
c(1)
SHG in MoS2 comparison with experiments from PRB 87, 201401(R) (2013), the electron-hole interaction enhances the SHG
Third-Harmonic Generation in a carbon nanoribon, compared with the imaginary part of the dielectric constant calculated at w and 3w
c(3)
Real and imaginary part of the THG of a 10x10 CNT along the z-direction
(comparison with experiments is working in progress)
resonance at w
resonance at 3w
h-BN
ZnO
GaN
SHG in two-dimensional
Hexagonal ZnO and GaN
We studied non-linear response of different nanostructure by means of a novel and efficient approach in real-time. We showed that excitons play a major role not only in the linear response but also in the non-linear one due to the reduce dimensionality and the poor screening.