Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals

By sidestepping the intractable calculations of many-body wavefunctions, density functional theory (DFT) has revolutionized the prediction of ground states of materials. However, predicting nonlinear responses–critical for next-generation quantum devices–still relies heavily on explicit wavefunctions, limiting computational efficiency. In this letter, using the circular photogalvanic effect (CPGE) in Weyl semimetals as a representative example, we realize a 1000-fold computational speedup by eliminating the explicit dependence on wavefunctions. Our approach leverages the one-to-one correspondence between free parameters of Weyl fermions and the associated responses to obtain precise wavefunction-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 wavefunction-free formula for the Berry-curvature dipole in Weyl semimetals. Our work paves the way for substantially more efficient screening and optimization of nonlinear electromagnetic properties in topological quantum materials.

💡 Research Summary

In this paper the authors introduce a wavefunction‑free methodology for calculating nonlinear electromagnetic responses in Weyl semimetals, using the circular photogalvanic effect (CPGE) as a benchmark. Traditional first‑principles workflows for CPGE involve three steps: (i) density‑functional theory (DFT) band‑structure calculation, (ii) construction of a Wannier‑based tight‑binding model, and (iii) evaluation of the CPGE tensor by integrating Bloch wavefunctions over the Brillouin zone. The third step is computationally prohibitive, often requiring ~10⁶ seconds of CPU time and several terabytes of memory.

The key insight of the work is that for a given class of quasiparticles—here the low‑energy Weyl fermion—the entire wavefunction geometry is uniquely determined by a small set of Hamiltonian parameters: the anisotropic velocities ν_i, the tilt vectors ν_ti, the chemical potential μ, and possible higher‑order warping coefficients δ_i. By analytically integrating the standard CPGE expression (Eq. 1) over momentum space with these parameters, the authors derive closed‑form, purely algebraic expressions for the transverse CPGE components β_ab (a = b). For a tilted type‑I Weyl node (tilt magnitude W_T < 1) the result is

β_ab = (3e³C/πh²) · (ν_ta ν_tb / ν_b² W_T²) · Λ₁(ℏω) ·