Anomalous suppression of higher-order nonlinearities in 3D Dirac semimetals

Three dimensional Dirac semimetals are often thought to share the same essential physics as 2D Dirac materials. Here, we present a counter-intuitive feature of 3D Dirac semimetals that sets them apart from their 2D counterparts: the absence of field-induced intraband nonlinearities beyond the third order at zero temperature at or near a critical field strength. Our closed-form intraband current expressions show that this effect is robust against changes in incident field polarization and phase, and remains significant at finite temperatures. Our theory is in excellent agreement with nonperturbative numerical simulations of the field-induced electron dynamics. Additionally, we identify regimes where 3D Dirac semimetals effectively function as bulk versions of 2D Dirac semimetals with the potential for superior performance in terms of high-harmonic generation. Our work fills a vital gap in understanding the nonlinear response of bulk Dirac electrons, and paves the way for the development of chip-integrable, nanophotonic devices and optoelectronics based on Dirac materials.