We study the interplay between stripes and $d$-wave superconductivity in the two-dimensional $t-t^{\prime }-J$ model using a variational Monte Carlo method. The next-nearest-neighbor hopping $t^{\prime }<0\mathrm{}$ stabilizes the stripe states around $1/8$ hole doping rate. We find that stripes and spatially oscillating superconductivity coexist depending on parameters. The superconducting orders are enhanced at the hole stripe regions. Although the energy differences are relatively small, the stripe state in which the phases between adjacent superconducting stripes are the opposite (antiphase) is also stabilized. We consider the possibility that the antiphase coexistence may explain the weakness of the $c$-axis Josephson couplings in the ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$.

• Received 19 November 2000

DOI:https://doi.org/10.1103/PhysRevLett.88.117001