Disorder perturbations of topological superconductor surface fluids: Semiclassical geodesic approach*

At the boundary of the simplest type of bulk topological superconductor, electric impurity potentials couple gravitationally to the stress tensor of the surface Majorana cone. While weak disorder is irrelevant near the Dirac point, recent numerics uncovered an unexpected result: the finite energy states form “stacks” of statistically identical, quantum critical wave functions [1].

We study the geometric properties of these manifolds, which are dominated by curvature singularities that differ starkly from our own cosmology. We find that nematic fluctuations have a profound effect on the spacetime geometry. These precipitate domain walls of curvature singularities that carve the space into disjoint regions. On one hand, nematic fluctuations create bound-state orbits along these walls. At the same time, we identify a collimating effect, allowing impinging geodesics to pass through the walls at certain “magic angles.” By contrast, isotropic singularities occur at isolated points and simply capture geodesics. We discuss statistical properties of the null geodesics and interesting toy models in both the semiclassical and quantum pictures.

[1] Ghorashi, Karcher, Davis, Foster, PRB 101, 214521 (2020).