Event Details

It is usually believed that increasing disorder strength in a d>2-dimensional system leads to the Anderson localisation transition with universal properties depending only on the space dimensionality. We demonstrate that systems with a power-law quasiparticle dispersion **\xi_{\bf k}\propto k^\alpha** in dimensions **d>2\alpha** exhibit another type of 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 conductivity and the density of states, we calculate the critical behaviour (exponents and scaling functions), using a renormalisation group, controlled by an $varepsilon=2alpha-d$ expansion. We also discuss how this novel transition can be observed in 3D Weyl semimetals and in recently realised 1D and 2D arrays of ultracold trapped ions with power-law interactions.