Interference evidence for Rashba-type spin splitting on a semimetallic $\mathrm{WT}{\mathrm{e}}_2$ surface

Semimetallic tungsten ditelluride displays an extremely large nonsaturating magnetoresistance, which is thought to arise from the perfect $n-p$ charge compensation with low carrier densities in $\mathrm{WT}{\mathrm{e}}_2$. We find a strong Rashba spin-orbit effect in density functional calculations due to the noncentrosymmetric structure. This lifts twofold spin degeneracy of the bands. A prominent umklapp interference pattern is observed by our scanning tunneling microscopic measurements at 4.2 K, which differs distinctly from the surface atomic structure demonstrated at 77 K. The energy dependence of umklapp interference shows a strong correspondence with densities of states integrated from ARPES measurement, manifesting a fact that the bands are spin-split on the opposite sides of Γ. Spectroscopic survey reveals the electron/hole asymmetry changes alternately with lateral locations along the $b$ axis, providing a microscopic picture for double-carrier transport of semimetallic $\mathrm{WT}{\mathrm{e}}_2$. The conclusion is further supported by our ARPES results and Shubnikov–de Haas (SdH) oscillations measurements.

Figure 1

Calculated electronic structures of $\mathrm{WT}{\mathrm{e}}_2$. (a) The relaxed bulk structure of $\mathrm{WT}{\mathrm{e}}_2$. (b) The calculated band structure of $\mathrm{WT}{\mathrm{e}}_2$ bulk, with relaxed structure of the slab. (c) The photoemission intensity plot (left panel) along the $\mathrm{\Gamma }-X$ direction together with a closer inspection of the calculated electronic structure (right panel). The colorful lines are the schematic drawings of the low-lying electronic structure of $\mathrm{WT}{\mathrm{e}}_2$. (d) Calculated 3D Fermi surface for $\mathrm{WT}{\mathrm{e}}_2$ bulk. Fermi surfaces for the five bands crossing the Fermi level shown as blue for hole surfaces and red for electron surfaces. The bottom right panel shows the total Fermi surface.

Figure 2

STM/S measurements of cleaved $\mathrm{WT}{\mathrm{e}}_2$. (a) Atomically resolved STM topographic image of the cleaved $\mathrm{WT}{\mathrm{e}}_2$ surface acquired at 77 K. (b) Top view of crystal structure of $\mathrm{WT}{\mathrm{e}}_2$. Top Te(i) and Te(o) atoms are highlighted by red circles. (Right panel) FFT image of (a), displaying Bragg vectors and the corresponding first Brillouin zone (purple rectangle). (c) The calculated total DOS, with projections of the DOS onto different atoms, W ($d$ orbitals) and Te ($p$ orbitals). The energy zero is set to the Fermi level. (d) $dI/dV$ spectrum acquired on the $\mathrm{WT}{\mathrm{e}}_2$ surface. Setpoint parameters: $V_b=+50\mathrm{mV}$ (a), $R_J=0.5\mathrm{G}\mathrm{\Omega }$; $V_{\mathrm{rms}}=5\mathrm{mV}$. (Inset) Schematic band structure of $\mathrm{WT}{\mathrm{e}}_2$.

Figure 3

STM images and tunneling spectra obtained at 4.2 K. (a) STM topographic image, $V_b=500\mathrm{mV}, I=100\mathrm{pA}$. (b) (Left) STM images taken at 77 and 4.2 K. (Right) Schematic drawing showing umklapp-type interference processes in spin-conserving processes. (c) $dI/dV$ image with $V_b=-100\mathrm{mV}, I=100\mathrm{pA}$. The size of image is $10\mathrm{nm}\times 10\mathrm{nm}$. (d) FFT pattern of the image shown in (c). (e) The energy dependence of the intensities for vector $\overrightarrow{g_b},\overrightarrow{g_a}$ and $\overrightarrow{g_b}+\overrightarrow{g_a}$, respectively. (f) A schematic illustration for bands near $E_F$ along the Γ-$X$ direction with the integrated DOS (thick black line) from ARPES data.

Figure 4

$dI/dV$ spectra obtained at 4.2 K. (a) A series of $dI/dV$ spectra acquired along the blue line in Fig. 3. $V_b=50\mathrm{mV}, I=100\mathrm{pA}, V_{\mathrm{rms}}=5\mathrm{mV}$. (b) A grayscale plot of these $dI/dV$ curves with the tip displacement. (c) The calculated ratio of electron/hole asymmetry based on the spectra survey in (a).