Uncovering the Fourier Structure of Wavefunctions in Semiconductors

TL;DR

This paper explores the Fourier structure of wavefunctions in semiconductors, revealing how symmetry influences degeneracies and optical properties, and simplifying the analysis of nonlinear optical responses.

Contribution

It uncovers the Fourier structure of wavefunctions in semiconductors and links symmetry-induced degeneracies to optical properties and nonlinear responses.

Findings

Wavefunctions are predominantly single planewaves in the Brillouin zone.

Symmetry determines degeneracy lifting and interaction potentials.

Nonlinear optical responses originate from higher order degeneracies.

Abstract

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.