Unusual magnetotransport from Si-square nets in topological semimetal HfSiS

The class of topological semimetals comprises a large pool of compounds. Together they provide a wide platform to realize exotic quasiparticles, for example, Dirac, nodal-line Dirac, and Weyl fermions. In this Rapid Communication, we report the Berry phase, Fermi-surface topology, and anisotropic magnetoresistance of HfSiS which has recently been predicted to be a nodal-line semimetal. This compound contains a large carrier density, higher than most of the known semimetals. Massive amplitudes of de Haas–van Alphen and Shubnikov–de Haas oscillations up to 20 K in 7 T assist us in witnessing a nontrivial π-Berry phase, which is a consequence of topological Dirac-type dispersion of bands originating from the hybridization of $p_x+p_y$ and $d_{x^2-y^2}$ orbitals of square-net plane of Si and Hf atoms, respectively. Furthermore, we establish the three-dimensional Fermi surface which consists of very asymmetric water caltroplike electrons and barley seedlike hole pockets which account for the anisotropic magnetoresistance in HfSiS.

Figure 1

For $B\left|\right|\left[100\right]$, (a) isothermal magnetization at different temperatures, (b) amplitude of dHvA after subtraction of background, and (c) temperature-dependent FFT amplitudes. Inset of (c) shows FFTs of oscillations mentioned in (b) that depict four frequencies α, β, γ, and η at 13.5, 120, 124, and 138.5 T, respectively. Corresponding data for the $B$||[001] case in (d), (e), and (f). In this case, FFTs show only two frequencies ε and ζ at 31 and 264 T, respectively.

Figure 2

Fitting of the dHvA oscillations by the LK formula to determine the Berry phase for (a) α when $B\left|\right|\left[100\right]$, (c) ε, and (d) ξ when $B\left|\right|\left[001\right]$, where the black line is measured data and the red line is fit. (b) shows the beating patterns that contain closely observed β, γ, and η frequencies.

Figure 3

(a) Magnetoresistance in different angles and their corresponding FFTs in (b) for $\theta =0^{\circ }-{90}^{\circ }$. (c) FFTs of SdH oscillations for $\varphi =0^{\circ }-{90}^{\circ }$. Rotation directions θ and ϕ are defined with respect to $B$ in the inset of (a).

Figure 4

(a) Experimentally observed frequencies (open circle) from SdH oscillations and theoretically calculated frequencies (blue cross for electron pocket and red cross for hole pocket), (b) 3D Fermi pockets (blue for electron and red for hole) in the first Brillouin zone, and (c) polar plots of ${\rho }_{xx}$ at 2 K in various fields when $I$ is always ⊥$B$ where, $0^{\circ }$ and ${90}^{\circ }$ correspond to $B$ along $c$- and $b$-axis, respectively.