Local construction of knotted screw dislocations in smectic liquid crystals

Abstract

The goal of this work is to show that, mathematically, screw dislocation loops with distinct topological properties can be introduced locally on a given smectic liquid crystal configuration. Concretely, given a configuration, we show that a new screw dislocation loop can be introduced along any knot or link transverse to the regular layers through a purely local modification. We define a topological invariant of screw dislocation loops, the multiplicity, and show that it can be explicitly prescribed in our construction. Finally, we apply this method to establish that any link type can be locally introduced within the set of screw dislocations of smectic configurations of a certain class. This shows that both the global topology (link type) and the local topology (multiplicity) of loop dislocations can be very rich, even when constrained to arise from local modifications.