Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures

We give an exact formulation for the transport coefficients of incommensurate twodimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C^* algebra framework introduced by Bellissard and collaborators [Coherent and Dissipative Transport in Aperiodic Solids, Lecture Notes in Physics (Springer, 2003), Vol. 597, pp. 413-486 and J. Math. Phys. 35(10), 5373-5451 (1994)] 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.