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

The magnetic phase diagrams, and other physical characteristics, of the hole-doped ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ and electron-doped ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_4$ high-temperature superconductors are profoundly different. Given that it is envisaged that the simplest Hamiltonians describing these systems are the same, viz., the t-t’-J model, this is surprising. Here we relate these physical differences to their ground states’ single-hole quasiparticles, the spin distortions they produce, and the spatial distribution of carriers for the multiply doped systems. As is well known, the low doping limit of the hole-doped material corresponds to k=(π/2,π/2) quasiparticles, states that generate so-called Shraiman-Siggia long-ranged dipolar spin distortions via backflow. These quasiparticles have been proposed to lead to an incommensurate spiral phase, an unusual scaling of the magnetic susceptibility, as well as the scaling of the correlation length defined by ${\xi }^{\mathrm{-}1}$(x,T)=${\xi }^{\mathrm{-}1}$(x,0)+${\xi }^{\mathrm{-}1}$(0,T), all consistent with experiment. We suggest that for the electron-doped materials the single-hole ground corresponds to k=(π,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(q) for up to four carriers in small clusters.

Consistent with experiment, for the hole-doped materials short-ranged incommensurate spin orderings are induced, whereas for the electron-doped system only commensurate spin correlations are found. Further, we propose that there is an important difference between the spatial distributions of mobile carriers for these two systems: 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. Phase separation in this material is consistent with the midgap states found by recent angle-resolved photoemission spectroscopy studies. Last, we propose the extrapolation of an approach based on the t-t’-J model to the hole-doped 123 system.