Sets of unique continuation for heat equation

We study nodal lines of solutions to the heat equations. We are interested in the global geometry of nodal sets, in the whole domain of definition of the solution. The local structure of nodal sets is a well understander subject, while the global geometry of nodal lines is much less clear. We give a detailed analysis of a simple component of a nodal set of a solution of the heat equation

Nodal-link semimetals

In topological semimetals, the valence band and conduction band meet at zero-dimensional nodal points or one-dimensional nodal rings, which are protected by band topology and symmetries. In this Rapid Communication, we introduce "nodal-link semimetals", which host linked nodal rings in the Brillouin zone. We put forward a general recipe based on the Hopf map for constructing models of nodal-link semimetal. The consequences of nodal ring linking in the Landau levels and Floquet properties are investigated.Comment: 12 pages, 5 figures, including supplemental material. Published versio