  The effect of the additional second neighbor hopping t' on the charge
dynamics of the t-J model in the underdoped regime is studied within the
fermion-spin theory. The conductivity spectrum of the t-t'-J model shows the
low-energy peak and unusual midinfrared band, while the resistivity exhibits a
nearly temperature linear dependence with deviation at low temperature in the
underdoped regime. Although the qualitative feature of the charge dynamics in
the t-t'-J model is the same as in the case of the t-J model, the additional
second neighbor hopping t' leads to a clear shift of the position of the
midinfrared band to the higher energies in the conductivity spectrum, and
suppress the range of the deviation from the temperature linear dependence in
the resistivity.
