Dispersion of a single hole in an antiferromagnet

We revisit the problem of the dispersion of a single hole injected into a quantum antiferromagnet. We applied a spin-density-wave formalism extended to a large number of orbitals and obtained an integral equation for the full quasiparticle Green's function in the self-consistent " noncrossing" Born approximation. We found that for t/J much greater than 1, the bare fermionic dispersion is completely overshadowed by the self-energy corrections, In this case, the quasiparticle Green's function contains a broad incoherent continuum which extends over a frequency range of similar to 6t. In addition, there exists a narrow region of width O(JS) below the top of the valence band, where the excitations are mostly coherent, though with a small quasiparticle residue Z similar to J/t. The top of the valence band is located at (pi/2,pi/2). We found that the form of the fermionic dispersion, and, in particular, the ratio of the effective masses near (pi/2, pi/2) strongly depend on the assumptions one makes for the form of the magnon propagator. We argue in this paper that two-magnon Raman scattering as well as neutron-scattering experiments strongly suggest that the zone-boundary magnons are not free particles since a substantial portion of their spectral weight is transferred into an incoherent background. We modeled this effect by introducing a cutoff q(c) in the integration over magnon momenta. We found analytically that for small q(c), the strong-coupling solution for the Green's function is universal, and both effective masses are equal to (4JS)(-1). We further computed the full fermionic dispersion for J/t = 0.4 relevant for Sr2CuO2Cl2, and t' = -0.4J and found not only that the masses are both equal to (2J)(-1), but also that the energies at (0,0) and (0,pi) are equal, the energy at (0,pi/2) is about half of that at (0,0), and the bandwidth for the coherent excitations is around 3J. All of these results are in full agreement with the experimental data. Finally, we found that weakly damped excitations only exist in a narrow range around (pi/2,pi/2). Away from the vicinity of (pi/2,pi/2), the excitations are overdamped, and the spectral function possesses a broad maximum rather than a sharp quasiparticle peak. This last feature was also reported in photoemission experiments.