Uncovering the Fourier Structure of Wavefunctions in Semiconductors

Symmetry is at the heart of material properties. Symmetry of the Bravais lattice defines the degeneracy of planewaves, upon which atomic symmetry determines interaction potentials which may lift such degeneracies. This results in wavefunctions which are single planewaves throughout the Brillouin zone (BZ), except in the vicinity of lifted degeneracies. This great simplification allows for determination of optical properties from a handful of planewaves and a single transition. Further, it reveals that nonlinear optical response arises from higher order degeneracy along lines/points in the BZ.