Phonon amplification in a graphite sheet under a microwave field

We study the atomic-displacement fluctuation in a graphite sheet under a microwave field by a modified functional integral approach. Our calculations show that the fluctuation continuously increases in some time ranges if the field strength and the frequency satisfy proper conditions. Since the atomic-displacement fluctuation is proportional to the phonon population number, this phenomenon may be considered as a phonon amplification effect led by a hopping electron–phonon coupling.