Quantum buckling.

We study the mechanical buckling of a freestanding superfluid layer. A topological defect in the phase of the quantum order parameter distorts the underlying metric into a surface of negative Gaussian curvature, irrespective of the sign of the defect charge. The resulting instability is in striking contrast with classical buckling, where the in-plane strain induced by positive (negative) disclinations is screened by positive (negative) curvature. We derive the conditions under which the quantum buckling instability occurs in terms of the dimensionless ratio between superfluid stiffness and bending modulus. An ansatz for the resulting shape of the buckled surface is analytically and numerically confirmed.