Bandwidth-disorder phase diagram of half doped layered manganites

Phase diagrams in the plane of $r_A$ (the average ionic radius, related to one-electron bandwidth $W$) and $sigma^2$ (the ionic radius variance, measuring the quenched disorder), or ``bandwidth-disorder phase diagrams, have been established for perovskite manganites, with three-dimensional (3$D$) Mn-O network. Here we establish the intrinsic bandwidth-disorder phase diagram of half-doped layered manganites with the two-dimensional (2$D$) Mn-O network, examining in detail the ``mother state of the colossal magnetoresistance (CMR) phenomenon in crystals without ferromagnetic instability. The consequences of the reduced dimensionality, from 3$D$ to 2$D$, on the order-disorder phenomena in the charge-orbital sectors are also highlighted.