Abstract
Structural distortion in a three-leg-ladder is studied in connection with Ludwigites, in particular the Fe and Co homometallic ones. Static impurities in t_{2g}-orbitals as infinite repulsion potentials randomly located in the three-leg-ladder and a Su-Schrieffer-Heeger like tight-binding Hamiltonian are proposed and discussed. It is found that such potentials block itinerant electrons and diminish a structural staggered order parameter, related with structural distortion, as 3^{-M} being M the number of impurities. This diminution is in detriment of Peierls like distortion that occurs in these ladders as in the case of Fe-Ludwigite. On the other hand, this diminution could explain the lack of structural distortion as in the case of Co-Ludwigite.
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