  We review recent numerical studies of two-dimensional (2D) Dirac fermion
theories that exhibit an unusual mechanism of topological protection against
Anderson localization. These describe surface-state quasiparticles of
time-reversal invariant, three-dimensional (3D) topological superconductors
(TSCs), subject to the effects of quenched disorder. Numerics reveal a
surprising connection between 3D TSCs in classes AIII, CI, and DIII, and 2D
quantum Hall effects in classes A, C, and D. Conventional arguments derived
from the non-linear $\sigma$-model picture imply that most TSC surface states
should Anderson localize for arbitrarily weak disorder (CI, AIII), or exhibit
weak antilocalizing behavior (DIII). The numerical studies reviewed here
instead indicate spectrum-wide surface quantum criticality, characterized by
robust eigenstate multifractality throughout the surface-state energy spectrum.
In other words, there is an "energy stack" of critical wave functions. For
class AIII, multifractal eigenstate and conductance analysis reveals identical
statistics for states throughout the stack, consistent with the class A integer
quantum-Hall plateau transition (QHPT). Class CI TSCs exhibit surface stacks of
class C spin QHPT states. Critical stacking of a third kind, possibly
associated to the class D thermal QHPT, is identified for nematic velocity
disorder of a single Majorana cone in class DIII. The Dirac theories studied
here can be represented as perturbed 2D Wess-Zumino-Novikov-Witten sigma
models; the numerical results link these to Pruisken models with the
topological angle $\vartheta = \pi$. Beyond applications to TSCs, all three
stacked Dirac theories (CI, AIII, DIII) naturally arise in the effective
description of dirty $d$-wave quasiparticles, relevant to the high-$T_c$
cuprates.
