Intensity of the first- and the second-order Raman spectra are calculated as
a function of the Fermi energy. We show that the Kohn anomaly effect, i.e.,
phonon frequency renormalization, in the first-order Raman spectra originates
from the phonon renormalization by the interband electron-hole excitation,
whereas in the second-order Raman spectra, a competition between the interband
and intraband electron-hole excitations takes place. By this calculation, we
confirm the presence of different dispersive behaviors of the Raman peak
frequency as a function of the Fermi energy for the first- and the second-order
Raman spectra, as observed in experiments. Moreover, the calculated results of
the Raman intensity sensitively depend on the Fermi energy for both the first-
and the second-order Raman spectra. These results thus also show the importance
of quantum interference effect phenomena.Comment: 9 pages, 10 figure