Systematic low-energy effective field theory for electron-doped antiferromagnets

Abstract

In contrast to hole-doped systems which have hole pockets centered at $(\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{2a},\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{2a})$, in lightly electron-doped antiferromagnets the charged quasiparticles reside in momentum space pockets centered at $(\frac{\ensuremath{\pi}}{a},0)$ or $(0,\frac{\ensuremath{\pi}}{a})$. This has important consequences for the corresponding low-energy effective field theory of magnons and electrons which is constructed in this paper. In particular, in contrast to the hole-doped case, the magnon-mediated forces between two electrons depend on the total momentum $\stackrel{P\vec}{P}$ of the pair. For $\stackrel{P\vec}{P}=0$, the one-magnon exchange potential between two electrons at distance $r$ is proportional to $1∕{r}^{4}$, while in the hole case, it has a $1∕{r}^{2}$ dependence. The effective theory predicts that spiral phases are absent in electron-doped antiferromagnets.