  To make the investigation of electronic structure of incommensurate
heterostructures computationally tractable, effective alternatives to Bloch
theory must be developed. In Massatt2017, we developed and analyzed a real
space scheme that exploits spatial ergodicity and near-sightedness. In the
present work, we present an analogous scheme formulated in momentum space,
which we prove have significant computational advantages in specific
incommensurate systems of physical interest, e.g., bilayers of a specified
class of materials with small rotation angles. We use our theoretical analysis
to obtain estimates for improved rates of convergence with respect to total CPU
time for our momentum space method that are confirmed in computational
experiments.
