Effect of the additional second neighbor hopping on the charge dynamics   in the t-J model
  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. 
Feng Yuan and Shiping Feng