(Submitted on 17 May 2017)
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.
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