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Abstract
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The present report is concerned with the dynamical behavior of -electronic valley states,
under the interaction with transverse zone-boundary optical phonons, in graphene. It is
assumed that the phonons are thermal and obey the Bose{Einstein distribution, while
the -electrons are initially prepared in an experimentally realizable particular valley
state. In our study, we take the view that such a mixture is completely described by a
time-dependent density operator which is then determined, to the second-order of perturbation,
from the governing Schrodinger equation. Employing the density operator so
calculated, an analytical expression for the valley polarization, as a function of time,
phonon frequency and temperature, is obtained. The results, accompanying with illustrative
gures, reveal that the -electrons, through the elastic exchange of energy with
phonons, change the valley states periodically with characteristics that strongly depend
upon the temperature. It is in particular shown that as the temperature is raised, the
time-averaged valley polarization approaches zero, as expected. Our calculations also
show that the amplitude of valley oscillations is solely determined by the temperature
and phonon frequency: an increase in the temperature enlarges the amplitudes in contrast
to the phonon frequency which does the reverse. Along these lines, moreover, we
demonstrate that the frequency of valley oscillations is determined by the electronic
momentum deviation from the valley states, along with the phonon frequency.
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