Deep Band Crossings Enhanced Nonlinear Optical Effects

Nonlinear optical (NLO) effects in materials with band crossings have attracted significant research interests due to the divergent band geometric quantities around these crossings. Most current research has focused on band crossings between the valence and conduction bands. However, such crossings are absent in insulators, which are more relevant for NLO applications. In this work, we demonstrate that NLO effects can be significantly enhanced by band crossings within the valence or conduction bands, which we designate as ``deep band crossings'' (DBCs). As an example, in two dimensions, we show that shift conductivity can be substantially enhanced or even divergent due to a mirror-protected ``deep Dirac nodal point''. In three dimensions, we propose GeTe as an ideal material where shift conductivity is enhanced by ``deep Dirac nodal lines''. The ubiquity of this enhancement is further confirmed by high-throughput calculations. Other types of DBCs and NLO effects are also discussed. By manipulating band crossings between arbitrary bands, our work offers a simple, practical, and universal way to enhance NLO effects greatly.