Wave-Function-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals

By sidestepping the intractable calculations of many-body wave functions, density functional theory has revolutionized the prediction of ground states of materials. However, predicting nonlinear responses-critical for next-generation quantum devices-still relies heavily on explicit wave functions, limiting computational efficiency. In this Letter, using the circular photogalvanic effect in Weyl semimetals as a representative example, we realize a 1000-fold computational speedup by eliminating the explicit dependence on wave functions. Our approach leverages the one-to-one correspondence between free parameters of Weyl fermions and the associated responses to obtain precise wave-function-free formulations. Applying our methodology, we systematically investigated known Weyl semimetals and revealed that Ta_{3}S_{2} exhibits photocurrents an order of magnitude greater than those observed in TaAs, with potential for an additional order-of-magnitude enhancement under strain. To further demonstrate the generality of our approach, we obtained a wave-function-free formula for the Berry-curvature dipole in Weyl semimetals. Our Letter paves the way for substantially more efficient screening and optimization of nonlinear electromagnetic properties in topological quantum materials.