Localization by virtual transitions in correlated disorder

Anderson localization is fundamentally relevant to all physical systems where coherent waves evolve in the presence of disorder. Physically, any disorder must have a finite spectral bandwidth, hence the disorder is always correlated. Here, we study the regime of localization mediated by virtual transitions in correlated disorder. We find that wave packets centered outside of the spectral extent of the disorder can localize, with localization length almost as short as for localization via first-order transitions. In this regime, virtual transitions lead to phenomena with profound significance, such as mobility edges, and strong localization in regions of momentum space where otherwise localization would be extremely weak. Remarkably, in two-dimensional systems, we show localization can occur in directions that cannot be reached by direct scattering from the disordered potential.