Generalized Kubo Formulas for the Transport Properties of Incommensurate   2D Atomic Heterostructures
  We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system. 
Eric Canc\`es, Paul Cazeaux and Mitchell Luskin
math-ph cond-mat.mtrl-sci math.MP