Wigner crystallization in Na$_3$Cu$_2$O$_4$ and Na$_8$Cu$_5$O$_{10}$ chain compounds.

We report the synthesis of novel doped edge-sharing chain compounds Na$_3$Cu$_2$O$_4$ and Na$_8$Cu$_5$O$_{10}$, which form insulating states with commensurate charge order [1]. We identify these systems as one-dimensional Wigner lattices, where the charge order is determined by the long-range Coulomb interaction and the number of holes in the d-shell of Cu. Our interpretation is supported by X-ray structure data as well as by an analysis of magnetic susceptibility and specific heat data. Remarkably, due to large second neighbor Cu-Cu hopping, these systems allow for an unambiguous distinction between the classical Wigner lattice and the $4k_F$ charge-density wave of quantum mechanical origin. Finally, we briefly discuss the domain-wall type charge excitations and the theoretical expectation for the optical conductivity of 1D Wigner lattices [2]. [1] P. Horsch, M. Sofin, M. Mayr, and M. Jansen, Phys. Rev. Lett. 94, 076403 (2005). [2] M. Mayr and P. Horsch, (unpublished).