  A d-wave high temperature cuprate superconductor exhibits a nematic ordering
transition at zero temperature. Near the quantum critical point, the coupling
between gapless nodal quasiparticles and nematic order parameter fluctuation
can result in unusual behaviors, such as extreme anisotropy of fermion
velocities. We study the disorder effect on the nematic quantum critical
behavior and especially on the flow of fermion velocities. The disorders that
couple to nodal quasiparticles are divided into three types: random mass,
random gauge field, and random chemical potential. A renormalization group
analysis shows that random mass and random gauge field are both irrelevant and
thus do not change the fixed point of extreme velocity anisotropy. However, the
marginal interaction due to random chemical potential destroys this fixed point
and makes the nematic phase transition unstable.
