  We study non-interacting systems with a power-law quasiparticle dispersion
$\xi_{\bf k}\propto k^\alpha$ and a random short-range-correlated potential. We
show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a
critical disorder strength (set by the band width), at which the system
exhibits a disorder-driven quantum phase transition at the bottom of the band,
that lies in a universality class distinct from the Anderson transition. In
contrast to the conventional wisdom, it manifests itself in, e.g., the
disorder-averaged density of states. For systems in symmetry classes that
permit localisation, the striking signature of this transition is a
non-analytic behaviour of the mobility edge, that is pinned to the bottom of
the band for subcritical disorder and grows for disorder exceeding a critical
strength. Focussing on the density of states, we calculate the critical
behaviour (exponents and scaling functions) at this novel transition, using a
renormalisation group, controlled by an $\varepsilon=2\alpha-d$ expansion. We
also apply our analysis to Dirac materials, e.g., Weyl semimetal, where this
transition takes place in physically interesting three dimensions.
