Laminar Flow of a Sheared Vortex Crystal: Scars in Flat Geometry
When we slowly shear a liquid, the local fluid velocity is proportional to the local force. This flow is possible because the molecules in a liquid are not ordered. Crystals are instead ordered and therefore do not flow at small stress, but deform elastically until the stress is large enough to cause plastic or irreversible flow that is usually localized on shear bands. At even larger stresses the flow can become laminar because of shear melting. Our simulations of two-dimensional vortex crystals at low temperature show that laminar flow can occur without melting: the crystal retains most of its ordered structure. This process is made possible by a suitable arrangement of topological defects in the lattice such as disclinations (a particle with five or seven neighbours) and dislocations (a pair of adjacent five-seven disclinations). As shown in the figure above disclinations (shaded cells) migrate in the interior of the disk while dislocations (pairs of dots) form radial walls or scars. Similar scars were observed in crystals arranged on curved surfaces, yielding an intriguing analogy between a sheared crystal in flat space and an equilibrium crystal in curved space.
At low currents we observe shear induced tearing of the triangular lattice, mediated by dislocations that are generated from the interior of the disk:
At higher currents the system transitions to laminar flow of the type described above (click here for a movie) whereby disclinations enter the interior of the system: