Anisotropic Fano resonance in the Weyl semimetal candidate LaAlSi

Topological Weyl semimetal (WSM) is a solid-state realization of chiral Weyl fermions, whose phonon behaviors provide in-depth knowledge of their electronic properties. In this work, anisotropic Fano resonance is observed in a type-II WSM candidate LaAlSi by polarized Raman spectroscopy. The asymmetric line shape occurs for the $B_1^2$ phonon mode of LaAlSi only for 488- and 532-nm laser excitations but not for 364-, 633-, and 785-nm excitations, suggesting the excitation selectivity. The asymmetry, frequency, and linewidth of the $B_1^2$ phonon mode, along with the spectral background, all show fourfold rotational symmetry as a function of the polarization angle in the polarized Raman spectra. While the shift of Raman frequency in a metal or semimetal is typically attributed to Kohn anomaly, here we show that the anisotropic frequency shift in LaAlSi cannot be explained by the effect of Kohn anomaly, but potentially by the anisotropic scattering background of Fano resonance. Origins of the excitation-energy dependence and anisotropic behavior of the Fano resonance are discussed by the first-principles calculated electronic band structure and phonon dispersion.

Figure 1

Crystal structure and Hall measurement of LaAlSi. (a) The powder x-ray diffraction of LaAlSi and the Rietveld refinement. The experimental data can be well fitted with the LaPtGe-type structure. Inset is the crystal structure of LaAlSi. (b) The Hall resistivity ${\rho }_{yx}$ as a function of magnetic field at different temperatures. (c) The Hall coefficients $R_{\mathrm{H}}$ (upper panel) and resistivity ${\rho }_{xx}$ (lower panel) as a function of temperature.

Figure 2

Raman-active phonon modes of LaAlSi. (a) Illustration of the Lorentz $\left(1/q=0\right)$ and Fano line shapes ($1/q=-0.2$ and −1). Other parameters in Eq. (1) are taken as $I_0=1$, ${\omega }_{\mathrm{BWF}}=0$, $\mathrm{\Gamma }=4$. (b) Raman spectra for the 364-, 488-, 532-, 633-, and 785-nm excitations. It is noted that the air signals due to high laser power are subtracted from the figure. (c) The enlarged spectra of the $B_1^2$ mode at 488 nm (top) and 532 nm (bottom) with the BWF fittings (black lines).

Figure 3

Color maps of Raman intensity for five excitations. The lower limit of the spectrometer for the 364-nm laser is around $140\mathrm{c}{\mathrm{m}}^{-1}$. The background spectra and air signals are subtracted from the Raman intensity.

Figure 4

Fano resonance of LaAlSi. (a) Raman spectra and color maps of the $B_1^2$ mode from $\theta ={45}^{\circ }$ to 135° for 532 nm. Background spectra are subtracted using a linear function of the Raman shift for a better view of the mode intensity. (b) $\left|1/q\right|$ of the $B_1^2$ mode for 532 nm. The polar plot is fitted using a sinusoidal function. (c) Polarization dependence of Raman frequency ${\omega }_0$ (left) and linewidth Γ (right) of the $B_1^2$ mode for 532 nm. (d)–(f) The same as (a)–(c) for 488 nm.

Figure 5

The continuous spectra for 532-nm excitation. (a) Raman spectra of LaAlSi from $\theta =0^{\circ }$ to 90°. The arrows show the evolution of the scattering background. (b) Polarization dependence of the scattering background.

Figure 6

Electronic band structure and phonon dispersion of LaAlSi. (a) Brillouin zone of LaAlSi. (b) Electronic band structure and density of states of LaAlSi. The green and blue arrows represent the excitation using laser energies of 532- and 488 nm, respectively. (c) Phonon dispersion and density of states of LaAlSi. Flatbands around 100–120 and $160–200\mathrm{c}{\mathrm{m}}^{-1}$ are highlighted.