== Symmetry Analysis of Phonons in 4H-SiC

The phonons at the #sym.Gamma point in 4H-SiC (space group P6#sub[3]mc)
  corresponds to four irreducible representations of C#sub[6v] point group
  (4A#sub[1] + 4B#sub[1] + 4E#sub[1] + 4E#sub[2]),
  including translational movement (1A#sub[1] + 1E#sub[1]), strong polar modes (1A#sub[1] + 1E#sub[1]),
  and negligible-polar modes (2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2]).
// The form of the Raman tensors for each representation is well known and summarized in @table-rep.

// #include "table-rep.typ"

By further decomposing the doubly degenerate modes (E#sub[1] and E#sub[2] of C#sub[6v] group)
  into the C#sub[2v] point group,
  the raman scattering corresponding to vibration along x and y directions could be distinguished.
For example, the E#sub[2] peeks observed in the Raman experiment of z(yy)#overline[z]
    correspond to phonons vibrating along the y direction,
  while the E#sub[2] peeks observed in z(yx)#overline[z] correspond to phonons vibrating along the x direction.
This is important when the x and y directions become inequivalent and the double degeneracies are slightly lifted.