  We numerically study weak, random, spatial velocity modulation ["quenched
gravitational disorder" (QGD)] in two-dimensional massless Dirac materials. QGD
couples to the spatial components of the stress tensor; the gauge-invariant
disorder strength is encoded in the quenched curvature. Although expected to
produce negligible effects, wave interference due to QGD transforms all but the
lowest-energy states into a quantum-critical "stack" with universal,
energy-independent spatial fluctuations. We study five variants of velocity
disorder, incorporating three different local deformations of the Dirac cone:
flattening or steepening of the cone, pseudospin rotations, and nematic
deformation (squishing) of the cone. QGD should arise for nodal excitations in
the $d$-wave cuprate superconductors (SCs), due to gap inhomogeneity. Our
results may explain the division between low-energy "coherent"
(plane-wave-like) and finite-energy "incoherent" (spatially inhomogeneous)
excitations in the SC and pseudogap regimes. The model variant that best
matches the cuprate phenomenology possesses quenched random pseudospin
rotations and nematic fluctuations. This model variant and another with pure
nematic randomness exhibit a robust energy swath of stacked critical states,
the width of which increases with increasing disorder strength. By contrast,
quenched fluctuations that isotropically flatten or steepen the Dirac cone tend
to produce strong disorder effects, with more rarified wave functions at low-
and high-energies. Our models also describe the surface states of class DIII
topological SCs.
