Cover of EPJ B’s June issue is illustrated by the main figure of article « Topology of contact points in Lieb-kagomé model », by Gilles Abramovici.
This object, called classification surface, is a powerful device giving topological properties of the energy band structure. Topological determination has become a key approach in many physical systems, like graphene or superconducting materials exhibiting Majorana states. Here, the model relies to the topological classification of contact points of Lieb-kagomé three-band model; its interpolates continuously Lieb model, where there is a simultaneous contact of the three energy bands, and kagomé one, where two Dirac points (contact points forming cylindrical cones joining at their extremity) have merged into a parabolic contact point.
In Lieb-kagomé model, the topology gives the winding numbers of all singularities, associated to Dirac points and allows an exact description of their merging. For instance, the numbers associated to both Dirac points about to join are +1, while that of the parabolic contact is +2. If this numbers had been opposite, +1 and -1, the singularities would have annihilated each other by joining. It has also clarified the particular case of the singularity in Lieb model, where the merging process is more elaborate. This work has shown that the singularities do not add because their number are not defined in the same space.
The cover image represents a 4-dimension object, whose holes allow the characterization of any non-trivial path in reciprocal space (kx, ky). It shows its intersection with sphere S3, which provides a 3-dimensional view.
Topology of contact points un Lieb-kagomé model
The European Physical Journal B, 2021, 94, 132
doi : 10.1140/epjb/s10051-021-00113-y