Multiple Weyl fermions in the noncentrosymmetric semimetal LaAlSi

The noncentrosymmetric $R\mathrm{Al}\mathit{Pn}$ ($R=\mathrm{rare}\mathrm{earth}, Pn=\mathrm{Si}$, Ge) family, predicted to host nonmagnetic and magnetic Weyl states, provides an excellent platform for investigating the relation between magnetism and Weyl physics. By using high-field magnetotransport measurements and first principles calculations, we have unveiled herein both type-I and type-II Weyl states in the nonmagnetic LaAlSi. By a careful comparison between experimental results and theoretical calculations, nontrivial Berry phases associated with Shubnikov–de Haas oscillations are ascribed to the electron Fermi pockets related to both types of Weyl points located ∼0.1 eV above and exactly on the Fermi level, respectively. Under high magnetic field, signatures of Zeeman splitting are also observed. These results indicate that, in addition to the importance for exploring intriguing physics of multiple Weyl fermions, LaAlSi as a comparison with magnetic Weyl semimetals in the $R\mathrm{Al}\mathit{Pn}$ family would also yield valuable insights into the correlation between magnetism and Weyl physics.

Figure 1

(a) Powder x-ray diffraction and Rietveld refinement result of LaAlSi. Insets: an image of a typical single crystal with clean (001) plane and the schematic crystal structure. (b),(c) Longitudinal ${\rho }_{xx}$ and Hall resistivity versus low magnetic field $B$ in the temperature range of 2–150 K. Inset of (c) shows the longitudinal resistivity versus temperature. (d) The calculated carrier density and mobility versus temperature.

Figure 2

(a) The longitudinal magnetoresistance versus magnetic field, which displays clear quantum oscillations under high magnetic field. Inset shows two more peaks at ∼18 and 32 T in addition to the main peaks. (b) The SdH oscillatory component as a function of 1/$B$ after subtracting the background. The inset shows the enlarged views for the quantum oscillations of $F_{\beta }$. (c) FFT spectra of $\mathrm{\Delta }{\rho }_{xx}$ show the obtained two fundamental frequencies $F_{\alpha }=7.96\mathrm{T}$ and $F_{\beta }=47.78\mathrm{T}$. (d) Temperature dependence of relative FFT magnitude of the two fundamental frequencies. The solid lines denote the fitting by using the LK formula. (e) Landau level indices of $F_{\beta }$ extracted from the SdH oscillations plotted as a function of 1/$B$. The solid line indicates the linear plots to the data. Inset: Dingle plot of the SdH oscillation at $T=2\mathrm{K}$.

Figure 3

(a) Longitudinal ${\rho }_{xx}$ and $–d^2{\rho }_{xx}/d{B}^2$ oscillation component versus magnetic field $B$ at 2 K. Inset: $–d^2{\rho }_{xx}/d{B}^2$ oscillation component at different $T$. (b) Landau fan diagram for the $F_{\beta }$ with Zeeman splitting.

Figure 4

(a) Electronic band structure of LaAlSi without including the SOC. (b) Schematic illustration of the nodal rings in the Brillouin zone. (c) Fermi surfaces of LaAlSi over the bulk Brillouin zone. (d) Electronic band structure of LaAlSi including the SOC. (e)–(g) Band structures near the Weyl points ${\mathrm{W}}_1, {\mathrm{W}}_2$, and ${\mathrm{W}}_3$. (h) Evolution of the Wannier charge centers around the sphere enclosing W+ and W–. (i),(j) Weyl points in LaAlSi at $k_z=0$ and $k_z={\mathrm{W}}_2$ planes labeled by cyan/magenta dots with different chiralities.

Figure 5

(a) Longitudinal ${\rho }_{xx}$ versus magnetic field $B$ at different angles between $B$ and the $c$ axis at 2 K. Inset shows the schematic measurement configuration. (b) SdH oscillatory component as a function of 1/$B$ at different angles. (c) FFT spectra of $\mathrm{\Delta }{\rho }_{xx}$ at different angles. (d) Quantum oscillation frequencies as a function of the angle θ for the hole and electron FSs derived from experiments and calculations. Inset: Projection of three-dimensional FSs on the $k_x\text{−}{k}_y$ plane. The $F_{\alpha }$ and $F_{\beta }$ are marked by red arrows, which are connected to the Weyl cones corresponding to the ${\mathrm{W}}_2$ (green) and ${\mathrm{W}}_1$ (purple) Weyl points, respectively.