The role of Raman simulations in stacking order determination

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Table of contents

1 Raman spectroscopy in graphene and few-layer graphene 
1.1 Carbon-based Materials
1.2 Properties of graphene and few-layer graphene systems
1.2.1 The adiabatic approximation
1.2.2 Electronic properties
1.2.3 Vibrational properties
1.2.4 Kohn anomalies
1.3 Raman scattering
1.4 Raman spectroscopy in graphene
1.4.1 Uniaxial strain
1.4.2 Doping
1.4.3 Edges, defects and disorder
1.4.4 Counting the number of layers
1.5 Stacking order determination in few-layer graphene
1.6 The role of Raman simulations in stacking order determination
2 Raman simulations and challenges 
2.1 Theory of Raman scattering : An overview
2.1.1 Second quantization for electrons and phonons
2.1.2 Electron-phonon coupling
2.1.3 Electron-photon coupling
2.1.4 Second order Raman scattering
2.2 Electron correlations effects beyond LDA
2.2.1 Effects on electron energies
2.2.2 Effects on phonon frequencies and the electron-phonon coupling
2.3 Difficulties of ab-initio resonant Raman calculation
3 Calculation of Raman intensities using the Wannier interpolation scheme and the BZ reduction method 
3.1 Wannier interpolation
3.1.1 Maximally localized Wannier functions
3.1.2 Wannier Interpolation schemes
3.1.3 Summary of Wannier interpolation
3.1.4 Case study : single and double layer graphene
3.2 Reduction method
3.2.1 General formulation
3.2.2 Case study : single and double layer graphene
3.3 General procedure for Raman simulations
3.4 Tests of Raman simulations in single and double layer graphene
4 Application for 2D systems : trilayer and tetralayer graphene
4.1 State-of-the-art of Raman simulation in few-layer graphene
4.2 Electron bands dispersion
4.3 Phonon frequencies
4.4 Calculated spectra
4.5 Analysis of trilayer graphene Raman spectra
4.6 TO branch dispersions from Raman spectra in trilayer graphene
4.7 The Difference between ABA and ABC trilayers 2D peaks
4.8 Conclusion
5 Application for 3D systems : Bernal and rhombohedral graphites 
5.1 State-of-the-art of Raman simulation in graphite
5.2 Electron bands and phonon frequencies
5.3 Calculated spectra : the Raman fingerprint of rhombohedral graphite 
5.4 Width of the 2D peak in AB and ABC-stacked graphite
5.5 Spectra analysis of AB-stacked graphite
5.6 TO phonon bands dispersion from Raman spectra
5.7 Conclusion
Conclusions and perspectives
Appendices 
A Inclusion of electron correlations effects
B Goldstone diagrams for double resonant Raman scattering 
C TO-character calculation 
D Spectra analysis at higher excitation energies