One-sided stripe supersolidity from engineered non-axisymmetric dipolar interactions

A supersolid combines density order with phase coherence, and doped lattice solids ask whether added defects can become coherent without melting the ordered background. We study a soft-core Bose-Hubbard model with isotropic hopping and an engineered non-axisymmetric dipolar interaction, $V_{ij}=V_2(x_{ij}^2-y_{ij}^2)/r_{ij}^5+W_6/r_{ij}^6$, where the sign-changing $d_{x^2-y^2}$ component selects a fixed $(q,0)$ stripe channel and the $W_6/r^6$ core stabilizes the short-distance attractive branch. Using sign-problem-free quantum Monte Carlo method with worm algorithm, we find that the half-filled stripe parent responds asymmetrically to doping: the hole side forms locked commensurate stripe solids with vanishing superfluid stiffness, whereas the particle side forms a stripe supersolid with finite compressibility $\kappa>0$, finite superfluid stiffness $\rho_s>0$, and enhanced double occupancy $D$. Keeping the same off-site kernel while increasing $U/t$ toward the hard-core limit shows that the particle-side supersolid disappears once doublon-like defects are projected out. Thus the engineered dipolar kernel selects the fixed $(q,0)$ stripe channel, while onsite softness selects the phase-coherent defect sector.