Multiple topologically nontrivial bands in noncentrosymmetric ${\mathrm{YSn}}_2$

The square lattices formed by main-group elements such as Bi, Sb, Sn, and Si in layered materials have attracted a lot of interest, since they can create rich topological phases. In this paper, we report the slightly distorted square lattice of Sn in a noncentrosymmetric compound ${\mathrm{YSn}}_2$ generates multiple topologically nontrivial bands, one of which likely hosts a nodal line and tunable Weyl semimetal state induced by the Rashba spin-orbit coupling and proper external magnetic field. The quasiparticles described as relativistic fermions from these bands are manifested by nearly zero mass and nontrivial Berry phases probed in de Haas-van Alphen (dHvA) oscillations. The dHvA study also reveals ${\mathrm{YSn}}_2$ has a complicated Fermi surface, consisting of several three-dimensional (3D) and one 2D pocket. Our first-principles calculations show the pointlike 3D pocket at Y point on the Brillouin zone boundary hosts the possible Weyl state. Our findings establish ${\mathrm{YSn}}_2$ as a new interesting platform for observing novel topological phases and studying their underlying physics.

Figure 1

(a) Crystal structure of ${\mathrm{YSn}}_2$. (b) Top view of Sn plane. (c) Distorted Sn layer of ${\mathrm{YSn}}_2$. (d) Single-crystal x-ray diffraction spectra of ${\mathrm{YSn}}_2$. Inset is an optical image of single-crystal ${\mathrm{YSn}}_2$.

Figure 2

(a) Isothermal out-of plane $(B//b$ axis) magnetization $M$ for ${\mathrm{YSn}}_2$ at various temperatures $\left(T=1.8\mathrm{K}–21\mathrm{K}\right)$. (b) Oscillatory magnetization after subtracting the background for $B//b$ in the 1.8–21 K temperature range. (c) The fits of the FFT amplitudes of the dHvA oscillations to the temperature damping factor $R_T$ in the LK formula. Inset shows the FFT spectra of the oscillatory magnetization for $B//b$. (d) The fit of the dHvA oscillation pattern at 1.8 K by the LK formula, with the solid line representing the fitted curve.

Figure 3

(a) and (d) The field dependence of magnetic torque $\tau$ for ${\mathrm{YSn}}_2$ at different temperatures from 1.7 K–50 K, which show strong dHvA oscillations. The magnetic field is applied nearly along the $b$ axis (a) and $ac$ plane (d). (b) and (e) show the FFT spectra of the oscillatory magnetization $\mathrm{\Delta }\tau$ for $B//b^{\prime }$ and $B//a{c}^{\prime }$, respectively. (c) and (f) show the fits of the FFT amplitudes by the temperature damping term $R_T$ of the LK formula.

Figure 4

(a) and (b) show the low-frequency $\left(F_{\alpha }\right)$ dHvA oscillations probed in magnetic torque for $B//b^{\prime }$ and $B//a{c}^{\prime }$, respectively, obtained after filtering the high-frequency components. (c) shows the high-frequency $(F_{\gamma }$ and $F_{\theta })$ oscillatory components of magnetic torque for $B//a{c}^{\prime }$, obtained after filtering the low-frequency components. The solid curves in (a), (b), and (c) represent the fits of the $T=1.7\mathrm{K}$ oscillation patterns by the single-/two-band LK formula.

Figure 5

(a) dHvA oscillations of isothermal magnetization $\left(M\right)$ for ${\mathrm{YSn}}_2$ at $T=1.8\mathrm{K}$ under different magnetic field orientations. (b) dHvA oscillations of magnetic torque of ${\mathrm{YSn}}_2$ at $T=1.8\mathrm{K}$ under different magnetic field orientations. The data of different $\theta$ have been shifted for clarity and the nonoscillating background has been subtracted. (c) The angular dependences of oscillation frequencies for ${\mathrm{YSn}}_2$. Inset: the experimental setup.

Figure 6

(a) Crystal structure for ${\mathrm{YSn}}_2$ with the space group of $Cmc{2}_1$. There is a distorted Sn lattice every two layers and a glide mirror ${\overline{M}}_{\mathrm{y}}\left\{\frac{1}{2},\frac{1}{2},0\right\}$ for ${\mathrm{YSn}}_2$. (b) Band dispersions for ${\mathrm{YSn}}_2$. The radius of red dots represents atomic projections from Sn in the Sn lattice. (c), (d) Magnified band dispersion of the $\alpha$ pocket along different directions. The two bands are nondegenerated along Γ-Y and Y-U directions and form a nodal line along the Y-T direction.

Figure 7

(a)–(c) shows the Fermi surface formed by the three pairs of bands around Fermi level. (d)–(e) shows the Fermi surfaces for ${\mathrm{YSn}}_2$ at $k_y=0$ and $k_y=\pi$ plane, respectively. (f) is the BZ for ${\mathrm{YSn}}_2$ and the green dashed line indicates the momenta of nodal line. (g) shows the magnification of the $\alpha$ pocket where the two red points are two crossing points along the T-Y direction. (i), (ii), (ii), and (iv) in (g) depict four possible paths of cyclotron orbitals for the Fermi pocket α for $B//b$.