Growth of a single stripe and a stripe phase from individual holes in the low-doping regime of a strongly correlated electron system

Abstract

In this paper, it is shown how a single stripe and a stripe phase grow from individual holes in the low-doping regime. In an effective low-energy description of the $t\text{\ensuremath{-}}J$ model, i.e., the phase-string model, a hole doped into the spin-ordered phase will induce a dipolar distortion in the background [Kou and Weng, 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 of 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.