  The unique terahertz properties of graphene has been identified for novel
optoelectronic applications. In a graphene sample with bias voltage added,
there is an enhanced absorption in the far infrared region and a diminished
absorption in the infrared region. The strength of enhancement(diminishment)
increases with the gate voltage, and the enhancement compensates the
diminishment. We find that it is the coherence length of electrons in graphene
that allows pure electronic transitions between states differing by small
momentums and makes intraband transition possible, is responsible for the far
infrared enhancement. Phonon assisted processes are not necessary and would not
in any case contribute to a sum rule. This naturally leads to results obeying
the general sum-rule in optical absorptions. Our prediction of the strength of
enhancement(diminishment) in terms of the bias agrees with experiments. This is
the first direct calculation we are aware of, since the prior phonon assisted
model for indirect transition should not obey a sum rule.
