Is there any hidden symmetry in the stripe structure of perovskite high temperature superconductors?

Local and fast structural probes using synchrotron radiation have shown nanoscale striped puddles and nanoscale phase separation in doped perovskites.It is known that the striped phases in doped perovskites are due to competing interactions involving charge, spin and lattice degrees of freedom,but while many theoretical models for spin and charge stripes have been proposed we are missing theoretical models describing the complex lattice striped modulations in doped perovskites. In this work we show that two different stripes can be represented as a superposition of a pair of stripes, U(theta_n) and D(theta_n), characterized by perovskite tilts where one of the pair is rotated in relation to the other partner by an angle Delta(theta _n)=pi/2. The spatial distribution of the U and D stripes is reduced to all possible maps in the well-known mathematical four-color theorem. Both the periodic striped puddles and random structures can be represented by using $planar$ graphs with a chromatic number. To observe the colors in mapping experiments, it is necessary to recover variously oriented tilting effects from the replica. It is established that there is an interplay between the annihilation/creation of new stripes and ordering/disordering tilts in relation to the theta _n angle in the CuO2 plane, where the characteristic shape of the stripes coincides with the tilting-ordered regions. By their origin, the boundaries between the stripes should be atomically sharp.
Comment: 6 pages, 4 figures