Inelastic scattering of visible light in graphene

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SUMMARY

The discussion centers on the inelastic scattering of visible light in graphene, specifically exploring its relationship to Raman spectroscopy. The participants highlight that while visible light scattering is analogous to the Compton effect observed with X-ray photons, the unique properties of graphene's massless electrons, characterized by the Hamiltonian H = -vf·σ·(p-eA/c), necessitate a different approach for calculating wavelength shifts. The Raman spectrum of graphene, as detailed in the referenced Phys. Rev. Lett. article, provides critical insights into the electronic structure and layer identification of graphene through its distinct peaks.

PREREQUISITES
  • Understanding of Raman spectroscopy and its application in material science.
  • Familiarity with quantum electrodynamics (QED) and perturbation theory.
  • Knowledge of graphene's electronic properties and Fermi velocity.
  • Basic principles of Compton scattering and its mathematical derivation.
NEXT STEPS
  • Study the principles of Raman spectroscopy in detail, focusing on its application to graphene.
  • Learn about the derivation of the Compton scattering formula and its implications for massless particles.
  • Investigate the Hamiltonian formulation of graphene and its significance in quantum mechanics.
  • Explore the impact of layer thickness on the Raman spectrum of graphene, particularly the D and G peaks.
USEFUL FOR

Researchers in material science, physicists studying quantum mechanics, and professionals involved in graphene technology development will benefit from this discussion.

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Inelastic scattering of Xray photons from electrons give them a wavelength shift, the Compton effect. The shift is inverse proportional with the mass of the electron. Now, if visible light scatters inelastic from electrons in graphene what will be the wavelength shift? The electrons in graphene 'behave' massless ...
Can this be calculated with QED using the graphene Hamiltonian H = -vf.sigma.(p-eA/c)?
Then we should calculate the perturbation up to second order?
Thanks! Claude.
 
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Inelastic scattering of visible light is usually referred to as Raman spectroscopy. Graphene being "hot", this has obviously been done.

One major difference between x-ray and neutrons vs. visible is that x-rays and neutrons carry momentum comparable to the Brillouin zone.

Phys. Rev. Lett. 97, 187401 (2006) [4 pages]
Raman Spectrum of Graphene and Graphene Layers

A. C. Ferrari1,*, J. C. Meyer2, V. Scardaci1, C. Casiraghi1, M. Lazzeri3, F. Mauri3, S. Piscanec1, D. Jiang4, K. S. Novoselov4, S. Roth2, and A. K. Geim4
1Cambridge University, Engineering Department, JJ Thompson Avenue, Cambridge CB3 0FA, United Kingdom
2Max Planck Institute for Solid State Research, Stuttgart 70569, Germany
3IMPMC, Universités Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France
4Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom

Received 9 June 2006; published 30 October 2006

Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers. The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process. The G peak slightly down-shifts. This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.

© 2006 The American Physical Society
URL:
http://link.aps.org/doi/10.1103/PhysRevLett.97.187401
DOI:
10.1103/PhysRevLett.97.187401
PACS:
78.67.Bf, 63.20.Dj, 63.20.Kr, 78.30.−j

*Electronic address: acf26@eng.cam.ac.uk
 
Here is my guess what happens:
The formula for Compton scattering is derived e.g. in Wikipedia:
http://en.wikipedia.org/wiki/Compton_scattering
In the case of a free massless particle, scattering would in deed be impossible.
However, the electrons in graphene, although formally massless, differ in one important
way from free massless particles: Their velocity is not c (light speed in vacuum) but some other value v, the Fermi velocity, which is much smaller. Hence the energy of an electron in graphene is not E=pc but E=pv.
If you carry trough the calculation you arrive at
[itex](f-f')^2 c^2/v^2=f^2+f'^2-2ff'\cos \theta[/itex]
 

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