Phase diagrams of (La,Y,Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$: Switching between the ladders and the chains

The most comprehensive charge response study of the intrinsically hole doped, spin-chain and spin-ladder composites is overviewed. Results of dc and electric-field-dependent resistivity, low frequency dielectric, and optical spectroscopy in all crystallographic directions are used to build phase diagrams of the underdoped materials (hole count$=6-y$ per formula unit, f.u.) and of the fully doped , 6 holes per f.u. The underdoped materials are insulators with hopping transport along the chains, which behave as a one-dimensional disordered system. For the fully doped materials the charge transport switches to the ladders due to transfer of holes from the chains. Two-dimensional (2D) charge-density wave (CDW) ground state is formed, i.e. besides CDW phason response along the ladders for $0\leq x \leq 9$, we also found it along the ladder rungs for $x \leq 6$. However, CDW sliding conductivity, as observed in the standard CDW materials, is not observed in either of directions. Normal to the ladder planes no CDW response was found, and transport is presumably hopping-like. For the first time in any system, CDW response away from the principal direction was identified. For $x > 9$ both CDW in ladders and CO in chains are supressed