Magnetic tilting and emergent Majorana spin connection in topological superconductors

Due to the charge-neutral and localized nature of surface Majorana modes, detection schemes usually rely on local spectroscopy or interference through the Josephson effect. Here, we theoretically study the magnetic response of a two-dimensional cone of Majorana fermions localized at the surface of class-DIII topological superconductors. For a field parallel to the surface the Zeeman term vanishes, and the orbital term induces a Doppler shift of the Andreev levels, resulting in a tilting of the surface Majorana cone. For fields larger than a critical threshold field H ∗ the system undergoes a transition from a type-I to type-II Dirac-Majorana cone. In a spherical geometry the surface curvature leads to the emergence of the Majorana spin connection in the tilting term via an interplay between orbital and Zeeman terms that generates a finite nontrivial coupling between negative- and positive-energy states. Majorana modes are thus expected to show a finite response to the applied field, which acquires a universal character in finite geometries and opens the way to detection of Majorana modes via time-dependent magnetic fields.