  Although Lorentz invariance forbids the presence of a term that tilts the
energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not
forbidden and, in fact, generic for condensed matter realizations of Weyl
semimetals. We here investigate the combined effect of such a tilted Weyl
dispersion and the presence of potential disorder. In particular, we address
the influence of a tilt on the disorder-induced phase transition between a
quasi-ballistic phase at weak disorder, in which the disorder is an irrelevant
perturbation, and a diffusive phase at strong disorder. Our main result is that
the presence of a tilt leads to a reduction of the critical disorder strength
for this transition or, equivalently, that increasing the tilt at fixed
disorder strength drives the system through the phase transition to the
diffusive strong-disorder phase. Notably this obscures the tilt induced
Lifshitz transition to an over tilted type-II Weyl phase at any finite disorder
strength. Our results are supported by analytical calculations using the
self-consistent Born approximation and numerical calculations of the density of
states and of transport properties.
