Analog black-hole creation on the surface of a topological superconductor

Bogoliubov quasiparticles on the surface of a topological superconductor are gapless Dirac fermions with a velocity that depends on the gap of the superconductor. If inhomogeneities are introduced on the surface, the effective metric of these fermions is affected (and in fact, for Class DIII, time-reversal invariant perturbations can only cause this type of disorder [1]). In extreme cases, the superconductivity can locally be destroyed on the surface, resulting in a vanishing velocity in a "dark spot." We discuss the dynamical process of this "dark spot" creation in analogy to a black hole formation. By performing the Hawking calculation in this 2D scenario, we highlight similarities and differences in the spacetime structure and particle creation at long times, far from the dark spot. With the full three-dimensional, UV completion, we discuss what occurs within the dark spot and the bulk of the material. Implications for the superconducting gap of the system near the surface are also discussed.

[1] Karcher, J. K. and M. S. Foster, Ann. Phys. 435 168439 (2021).