Band-theory description of hole localization and singlet polarons in doped cuprates

We use an advanced ab-initio band theory (the pseudo-self interaction corrected local density approach, pSIC) to describe spin-compensated polarons (e.g. Zhang-Rice singlets (ZRS)) typical of low-dimensional doped cuprates. Despite their many-body nature, ZRS can be transparently interpreted via (and, in fact, constructed from) single-particle states, provided that band theory describes accurately enough their localization in the limit of vanishing band dispersion. We provide examples of polarons in real materials, specifically chain-like Ca$_{2+x}$Y$_{2-x}$Cu$_{5}$O$_{10 }$and the high-T$_{c}$ superconductor (HTSC) Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{6+y}$. The former is the ideal prototype of dopable one-dimensional cuprate with zig-zag Cu-O interactions. Studying the electronic and magnetic properties over the full range of possible doping, we identify several different polaron-dominated ground states and the attendant phase transitions. Furthermore, ZRS are key to the behavior of doped CuO$_{2}$ units in HTSC. We show how their occurrence can dramatically affect the electronic properties (e.g. the Fermi surface) in underdoped Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{6+y}$.