The spin-ladder and spin-chain system (La,Y,Sr,Ca)14Cu24O41: Electronic phases,charge and spin dynamics

The quasi-one-dimensional cuprates (La,Y,Sr,Ca)₁₄Cu₂₄O₄₁, consisting of spin-chains and spin-ladders, have attracted much attention, mainly because they represent the first superconducting copper oxide with a non-square lattice. Theoretically, in isolated hole-doped two-leg ladders, superconductivity is tightly associated with the spin gap, although in competition with a charge-density wave (CDW). Indeed, both the gapped spin-liquid and CDW states have been established in the doped spin-ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$, however the relevance of these objects to electronic properties and superconductivity is still subject of intensive discussion. In this treatise, an appreciable set of experimental data is reviewed, which has been acquired in recent years, indicating a variety of magnetic and charge arrangements found in the chains and ladders of underdoped (La,Y)_y(S,Ca)_14−yCu₂₄O₄₁ and fully doped _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Based on these data, phase diagrams are constructed for the chains of underdoped systems (as a function of La, Y-substitution), as well as for the chains and ladders of the fully doped ones (as a function of Ca-substitution). We try to reconcile contradictory results concerning the charge dynamics in the ladders, like the hole redistribution between ladders and chains, collective modes and pseudogap, field-dependent transport and the temperature scales and doping levels at which the two-dimensional CDW develops in the ladder planes. The remaining open issues are clearly extracted. In the discussion the experimental results are contrasted with theoretical predictions, which allows us to conclude with two important remarks concerning the nature of the competing CDW and superconducting ground states. A density wave in ladders, characterized by a sinusoidal charge modulation, belongs to the class of broken symmetry patterns, which is theoretically predicted for strongly correlated low-dimensional electron systems; however its precise texture and nature is still an open issue. As for superconductivity, the presence of the spin gap in the normal state points towards d  -wave symmetry and magnetic origin of the attractive interaction. However, there is a finite density of mobile quasi-particles that appears for high Ca contents and increases with pressure, concomitantly with increased two-dimensionality and metallicity. For this reason the superconductivity in the doped ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ which occurs under high pressure cannot simply be a stabilization of the d-wave superconductivity expected for a pure single ladder system.