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

We consider the interplay between topology and disorder on the surface fluids of topological
superconductors (TSCs). In the case of a single 2D Majorana cone, only “quenched gravitational disorder
(QGD)” is allowed, i.e. a static modulation of the effective speed of light. Although disorder effects near
zero energy have been understood for a long time, recent numerical results uncovered an unexpected
result: finite energy TSC surface states form “stacks” of quantum critical wave functions, with universal,
energy-independent statistics [1,2,3]. In classes CI and AIII, one finds stacks of quantum Hall plateau
transition states [1,2]. For the single Majorana cone with QGD in class DIII, the stacked critical states
appear to belong to a new class [3]. In order to shed light on the DIII results, we consider a semiclassical
approach. We find that kinetic theory predicts a divergent conductivity at all temperatures. We further
study the statistical properties of the null geodesics in the 2+1-D quenched random spacetime metric
that can be associated to QGD.
[1] S. A. A. Ghorashi, Y. Liao, M. S. Foster, Phys. Rev. Lett. 121, 016802 (2018)
[2] B. Sbierski, J. Karcher, M. S. Foster, unpublished
[2] S. A. A. Ghorashi and M. S. Foster, arXiv:1903.11086