?
v
f
≈
10
6
?
m
s
)
are considered possible, even in relatively large sheets of graphene (10 μm and more). On the other hand, plasmons in graphene can have an exceptionally slow phase velocity, down to a few hundred times slower than the speed of light. Consequently, velocity matching between charge carriers and plasmons can be possible, allowing the emission of GPs from electrical excitations (hot carriers) at very high rates. This can pave the way to new devices utilizing the ?E on the nanoscale, a prospect made even more attractive by the dynamic tunability of the Fermi level of graphene. For a wide range of parameters, the emission rate of GPs can be significantly higher than the rates previously found for photons or phonons, suggesting that taking advantage of the ?E allows near-perfect energy conversion from electrical energy to plasmons.
In addition, contrary to expectations, plasmons can be created at energies above 2Ef—thus exceeding energies attainable by photon emission—resulting in a plasmon spectrum that can extend from terahertz to near infrared frequencies and possibly into the visible range.
Furthermore, tuning the Fermi energy by external voltage can control the parameters (direction and frequency) of enhanced emission. This tunability also reveals regimes of backward GP emission, and regimes of forward GP emission with low angular spread; emphasizing the uniqueness of ?E from hot carriers flowing in graphene.