An online seminar of the International Academic Cooperation project on the topic of Rashba's interaction, its derivation from the kinetic energy of the Schrödinger field, and the demonstration of linear quasiparticle dispersion was held on March 27, 2026.

The seminar is the second of two consecutive seminars dedicated to the problem of the connection of the Abrikosov-Bogomolny equations with the physics of topological effects. While the first seminar focused on the classical scalar case and laid the foundation for understanding self-dual vortex structures in type II superconductors, this seminar explores the Abrikosov-Bogomolny equations with the inclusion of spin degrees of freedom. The speaker: Mauro Doria, a member of the IAS project and a professor at the Federal University of Rio de Janeiro.

It has been demonstrated while the presentation,  that the Abrikosov-Bogomolny equations for the spinor field can be obtained from the kinetic energy of the Schrödinger spinor field. The key methodological approach is to decompose this contribution into three parts by representing the Laplace operator through the Lichnerowicz Laplacian, a geometric object that acts on spinors and takes into account the curvature of the bundle. This approach allows for a natural separation of the contributions from bulk and surface dynamics.
An important and non-trivial result is that in the spinor case, the above decomposition of the Schrödinger kinetic energy leads to the appearance of a surface term with the structure of a Rashba interaction. This spin-orbit interaction, localized at the interface, induces a linear Dirac spectrum of quasiparticles in the surface layer, which is a characteristic feature of topological phases of matter.
The discovered feature opens up an interesting and non-trivial possibility for unifying two seemingly different areas of condensed matter physics – the theory of topological insulators and the theory of type II superconductors. Since the Abrikosov-Bogoliubov equations find their natural application in both systems (describing vortices in superconductors and topologically protected surface states in insulators), the proposed approach allows us to look at them as manifestations of a single mathematical structure. This creates a conceptual bridge between the physics of vortex structures and the physics of topological phases, paving the way for the description of hybrid systems, such as topological superconductors with Majorana modes on vortices.