Superconductor Quasiparticles with Random Curvature, Robust Criticality, and T-Linear Resistivity

We study quenched random curvature disorder for 2D massless relativistic carriers. This describes a topological superconductor Majorana surface fluid with generic time-reversal invariant dirt. It should also apply to any non-topological Dirac or Majorana system in which the disorder is sufficiently smooth, as could be the case for d-wave quasiparticles in the cuprates with remote dopants.

Random curvature is strongly irrelevant at zero energy, but we show that it profoundly affects the finite-energy states. These are found to exhibit robust, universal criticality (see also Ghorashi, Liao, and Foster, PRL 2018). Our results imply that the local density of states imaged via STM would exhibit minimal spatial structure near zero bias, but robust, static and universal fluctuations over a large finite bias range.

We also consider a speculative connection to the pseudogap regime. Assuming that the superfluid component is quenched by phase fluctuations, we calculate the electrical conductivity. Preliminary results indicate linear-in-T resistivity, attributed to the crossover between ballistic and critical states at zero and finite-energy, respectively.