Quantum Buckling

Abstract

We study the mechanical buckling of a two dimensional membrane coated with a thin layer of superfluid. It is seen that a singularity (vortex or anti-vortex defect) in the phase of the quantum order parameter, distorts the membrane metric into a negative conical singularity surface, irrespective of the defect sign. The defect-curvature coupling and the observed instability is in striking contrast with classical elasticity where, the in-plane strain induced by positive (negative) disclinations is screened by a corresponding positive (negative) conical singularity surface. Defining a dimensionless ratio between superfluid stiffness and membrane bending modulus, we derive conditions under which the quantum buckling instability occurs. An ansatz for the resulting shape of the buckled membrane is analytically and numerically confirmed.

References in corpus (11)

• The electronic properties of graphene
• The structure of suspended graphene sheets
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Two-Dimensional Matter: Order, Curvature and Defects
• Graphene as an electronic membrane
• Gauge field induced by ripples in graphene
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Crystallography on Curved Surfaces
• Electron-induced rippling in graphene
• Defects in nematic membranes can buckle into pseudospheres
• Theory of the spontaneous buckling of doped graphene