Topological nodal line in ${\mathrm{ZrTe}}_2$ demonstrated by nuclear magnetic resonance

In this work, we report nuclear magnetic resonance (NMR) combined with density functional theory studies of the transition metal dichalcogenide ${\mathrm{ZrTe}}_2$. The measured NMR shift anisotropy reveals a quasi-two-dimensional behavior connected to a topological nodal line close to the Fermi level. With the magnetic field perpendicular to the ${\mathrm{ZrTe}}_2$ layers, the measured shift can be well-fitted by a combination of enhanced diamagnetism and spin shift due to high-mobility Dirac electrons. The spin-lattice relaxation rates with external field both parallel and perpendicular to the layers at low temperatures match the expected behavior associated with extended orbital hyperfine interaction due to quasi-two-dimensional Dirac carriers. In addition, calculated band structures also show clear evidence for the existence of a nodal line in ${\mathrm{ZrTe}}_2$ between $\mathrm{\Gamma }$ and $A$. For intermediate temperatures, there is a sharp reduction in spin-lattice relaxation rate that can be explained as due to a reduced lifetime for these carriers, which matches the reported large change in mobility in the same temperature range. Above 200 K, the local orbital contribution starts to dominate in an orbital relaxation mechanism revealing the mixture of atomic functions.

Figure 1

Crystal structure of $1T\text{−}{\mathrm{ZrTe}}_2$ with $P\text{−}3m1$ space group, showing van der Waals–bonded layered structure.

Figure 2

(a) ${}^{125}\mathrm{Te}$ line shapes of ${\mathrm{ZrTe}}_2$ at room temperature. (b) Angular dependence of shift at room temperature. The red solid curve is a fit to Eq. (1). Shift vs temperature for (c) $B\parallel c$ (magnetic field perpendicular to the layers) with linear and $ln\left(T\right)$ curves as guides to the eye and (d) $B\perp c$ (magnetic field parallel to the layers).

Figure 3

$1/T_{1}T$ vs $T$ for both orientations $B\parallel c$ (perpendicular to the layers) and $B\perp c$ (parallel to the layers). Inset: $1/T_{1}T$ vs $T$ in log scale.

Figure 4

Band structures of ${\mathrm{ZrTe}}_2$ with spin-orbit coupling, with superposed circles showing weights for (a) $p_x+p_y$ and (b) $p_z$ Te orbitals. The dashed lines represent the Fermi level. The circle size represents the partial state density of Te. (c) Density of states for ${\mathrm{ZrTe}}_2$. (d) 3D view of the hexagonal Brillouin zone with high-symmetry points. (e) Sketch of discrete nodal line between $\mathrm{\Gamma }$ and $A$.

Figure 5

(a) Sketch of Dirac band and electron pocket. (b) Simulated shifts for both orientations. Inset: chemical potential vs $T$. (c) $W=1/2T_1$ is the dipolar and orbital relaxation rates divided by $2\pi {\left({\gamma }_e{\gamma }_n{\hslash }^{3/2}\right)}^2{g}^2\left({\varepsilon }_F\right)k_{B}T{\langle r^{-3}\rangle }^2$. $\alpha$ is the mixture of orbitals ($p_x+p_y$) vs $p_z$.