The road from one hole to the stripe phase

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In this paper, it is shown how a single stripe and a stripe phase grow from individual holes in low doping regime. In an effective low-energy description of the t-J model, i.e., the phase string model, a hole doped into the spin ordered phase will induce a dipolar distortion in the background [Phys. Rev. B 67, 115103 (2003)]. We analyze the hole-dipole configurations with lowest energy under a dipole-dipole interaction and show that these holes tend to arrange themselves into a regular polygon. Such a stable polygon configuration will turn into a stripe as the number hole-dipoles becomes thermodynamically large and eventually a uniform stripe state can be formed, which constitutes an energetically competitive phase at low doping. We also briefly discuss the effect of Zn impurities on individual hole-dipoles and stripes.