  An explanation is proposed for the recently observed in optical spectra of
monolayer graphene giant increase in the Drude peak width under applied
uniaxial strain. We argue that the underlying mechanism of this increase can be
based on resonant scattering of carriers from inevitably present impurities
such as adsorbed atoms that can be described by the Fano-Anderson model. We
demonstrate that the often neglected scalar deformation potential plays the
essential role in this process. The conditions necessary for the maximum effect
of the giant Drude peak broadening are determined. It is stressed that the
effect is strongly enhanced when the Fermi level gets closer to the Dirac
point. Our theoretical analysis provides guidelines for functionalizing
graphene samples in a way that would allow to modulate efficiently the Drude
peak width by the applied strain.
