Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals

Abstract

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.

Figures (4)

• Figure 1: Our work involves obtaining closed-form expressions for nonlinear response tensors directly from Hamiltonian parameters, bypassing expensive wavefunction-based calculations, which makes it possible to greatly reduce computational costs while maintaining good accuracy.
• Figure 2: Left: dispersion and Berry curvature of a high symmetry Weyl fermion. Middle: Comparison of the CPGE from a high symmetry Weyl fermion and a Weyl fermion in TaAs. Right: dispersion and Berry curvature of a low symmetry Weyl fermion in TaAs.
• Figure 3: (a) Transverse CPGE of $\beta_{xy}$ (top) and $\beta_{zy}$ (bottom) and for $\vec{\nu}=(2,2,2)$(Å/s) for $\mu=20$ meV chemical potential. (b) Schematic of Pauli blocking of a tilted Weyl fermion. The red arrow indicates a representative electronic transition (filled blue circle) in the optical absorption region, highlighted with light coral color. These transitions are such that only a part of the spectrum is Pauli blocked within the photon energy interval $\epsilon_1<\hbar \omega<\epsilon_2$. (c) Function of $\sqrt{1-\Lambda_1^2}$ (top), $\Lambda_1\sqrt{1-\Lambda_1^2}$, and $\Lambda_1(1-\Lambda_1^2)^{3/2}$ (bottom) as function of photon energy for $\mu=-50$ meV chemical potential. Here, $\Lambda_1(\hbar\omega)$ is defined as $\frac{1}{\mathcal{W_T}} \left(\frac{2\mu}{\hbar\omega} - 1\right)$. (d) Transverse CPGE components $\beta_{xy}$ (top) and $\beta_{xy}\times \mathcal{W_T}^2$ (bottom) for $\vec{\nu} = (2, 2, 2)$ (Å/s) under two different sets of $\nu_x^t$. (e) The transverse CPGE of a type-I Weyl semimetal model for $\mu=-100$ meV chemical potential. The dotted line corresponds to our proposed formula of Eq. \ref{['Eq.tB']}, while the solid line shows the results of the numerical calculation from Eq. \ref{['CPGE_Org']}. (f) The transverse CPGE of a type-II Weyl semimetal model for a chemical potential of $\mu=-100$ meV are shown. The light orange color indicates the region where $\hbar \omega \geq \frac{2\mu}{\mathcal{W_T}-1}$.
• Figure 4: (a) Comparison of $\beta_{xy}$ calculations for sixteen near Fermi level Weyl points (inset) in TaAs with our present approach (dotted line) and conventional formulas (solid line). (b) The maximum frequency-dependent transverse CPGE $\beta_{xy}$ is compared with the results obtained for low photon energy. (c) This schematic illustrates the system where a laser is applied to the Ta$_3$S$_2$, with the strain indicated by arrows. (d) Up: Band dispersion of the Weyl node in Ta$_3$S$_2$ under various strain values. Down: Calculated maximum peaks of transverse CPGE (right-blue) $\beta_{xy}$ of Ta$_3$S$_2$ as a function of strain ($\eta$) in the [110] plane.