Interplay of electric field and disorder in Dirac liquid silicene

Layered materials with buckled structure offer a promising route to explore distinct phases of quantum matter. Using GGA + DMFT we reveal the complex interplay between perpendicular electric field and site-diagonal disorder in the Dirac liquid electronic state of silicene. The electronic structure we derive is promising in the sense that it leads to results that might explain why out-of-plane electric field plus moderate disorder can generate marginal Dirac valleys consistent with scanning tunneling spectroscopy of silicene on Ag substrates. Graphic Abstract

Renormalization to localization without a small parameter

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to generality of this model usually called Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.