Hole spectral functions in lightly doped quantum antiferromagnets

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional t-J and t-t'-t ''-J models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both t-J and t-t'-t ''-J models. Furthermore, our results show that the residue of the quasiparticle peak at (G) over right arrow = (+/-pi/2, +/-pi/2) decreases very rapidly with doping. We also find pockets centered at (G) over right arrow, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the t-J model and (ii) with an almost circular shape in the case of the t-t'-t ''-J model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.