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In the work we highlight the structural features of 2D perovskite cuprates(tilted CuO$_6$ octahedra with different orientation with respect to spacerrocksalt layers), where sources of charge and spin inhomogeneity can be hidden.We used the impurity Anderson model with the Jahn-Teller(JT) local cells toshow the charge inhomogeneity arises at any low doping concentration $x$, butdisappears when the doping level exceeds threshold concentration $x_c$, and thelower the magnitudes $x_c$, the more JT region square. It is expected thatspontaneous chiral symmetry breaking in the dynamic JT state of the stripeCuO$_2$ layer as a whole can lead to the appearance of the goldstone phononmode. As consequence, the giant thermal Hall effect could be observed in the 2Dperovskite cuprates with CuO$_6$ octahedra, rather than with CuO$_4$ squares,e.g. in Tl-based $n$ layer cuprates or cuprates based on the infinite-layerCaCuO$_2$ structure.

Lattice source for charge and spin inhomogeneity in 2D perovskite cuprates