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We study the magnetic susceptibility of a two-dimensional cone of Majoranamodes localised at the surface of a three-dimensional time-reversal invarianttopological superconductor belonging to class DIII. A field parallel to thesurface tilts the surface Majorana cone along the supercurrent direction. Forfields larger than a critical threshold field $H^*$, $H>H^*$, a transition fromtype I to type II Dirac cone occurs and a finite current carried by theMajorana modes start to flow, leading to an additional diamagnetic contributionto the surface magnetization. On a curved surface interband transitions arepromoted by the Majorana spin connection that couples to the external field,giving rise to a finite frequency magnetic susceptibility.

Signatures of surface Majorana modes in the magnetic response of topological superconductors