Role of Phonons, Doping and Domainwalls in Hole Propagation in Two-Dimensional Quantum Antiferromagnets

We study the two-dimensional (2D) t−J model (and its extensions) in order to understand the hole dynamics in the 2D CuO2 plane of the cuprate superconductors. Within the linear spin wave approximation (LSW) of the Hamiltonian and the non-crossing approximation (NCA) for the hole self energies, thermal broadening of the hole spectral peaks is investigated with and without the contribution of optical phonons. We find the string excitations [15] to survive even for relatively strong electron-phonon coupling. Experimental angle-resolved photoemission spectroscopy (ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling (ã). With vertex correction the agreement with experiment becomes possible even at a moderate value of ã. Finite hole doping in a 2D t−J model and its extensions at T = 0 is studied using NCA. Dressed hole and magnon Green's functions are obtained to analyze the hole energy bands/ Fermi surface topology and the magnon broadening and softening for the doped system. The doping-dependent staggered magnetization of the system is computed and the doping fraction up to which the staggered magnetization is non-zero is indicated. Contribution of the anomalous magnons has been reported as well. We also study the dynamics of a hole in a 2D lattice in a stripe-ordered background. Within the same LSW and NCA treatment to the t − J Hamiltonian we obtain the different spin wave modes and hole Green's functions of the superlattice structure. The hole spectra indicates the preference for the hole to be in the anti-phase domain wall rather than being within the antiferromagnetic block.