Theory of electron-hole asymmetry in doped {\em CuO$_2$} planes

The magnetic phase diagrams, and other physical characteristics, of the hole- doped {\em La$_{2-x}$Sr$_x$CuO$_4$} and electron-doped {\em Nd$_{2-x}$Ce$_x$ CuO$_4$} high-temperature superconductors are profoundly different. Starting with the $t-t^{\prime}-J$ model, the spin distortions and the spatial distri- bution of carriers for the multiply-doped systems will be related to the diffe- rent ground states' single-hole quasiparticles. The low doping limit of the hole-doped material corresponds to $\vec k = (\pi/2,\pi/2)$ quasiparticles, states that generate so-called Shraiman-Siggia long-ranged dipolar spin distor- tions via backflow. We propose that for the electron-doped materials the single- hole ground state corresponds to $\vec k = (\pi,0)$ quasiparticles; we show that the spin distortions generated by such carriers are short-ranged. Then, we demonstrate the effect of this single-carrier difference in many-carrier ground states via exact diagonalization results by evaluating $S(\vec q)$ for up to 4 carriers in small clusters. Also, the different single-carrier quasiparticles generate important differences in the spatial distributions: for the hole-doped material the quasiparticles tend to stay far apart from one another, whereas for the electron-doped material we find tendencies consistent with the clustering of carriers, and possibly of low-energy fluctuations into an electronic phase separated state. Lastly, we propose the extrapolation of an approach based on the $t-t^{\prime}-J$ model to the hole-doped 123 system.