Local Spectroscopic Characterization of Spin and Layer Polarization in ${\mathrm{WSe}}_2$

We report scanning tunneling microscopy and scanning tunneling spectroscopy (STS) measurements of monolayer and bilayer ${\mathrm{WSe}}_2$. We measure a band gap of $2.21\pm 0.08\mathrm{eV}$ in monolayer ${\mathrm{WSe}}_2$, which is much larger than the energy of the photoluminescence peak, indicating a large excitonic binding energy. We additionally observe significant electronic scattering arising from atomic-scale defects. Using Fourier transform STS, we map the energy versus momentum dispersion relations for monolayer and bilayer ${\mathrm{WSe}}_2$. Further, by tracking allowed and forbidden scattering channels as a function of energy we infer the spin texture of both the conduction and valence bands. We observe a large spin-splitting of the valence band due to strong spin-orbit coupling, and additionally observe spin-valley-layer coupling in the conduction band of bilayer ${\mathrm{WSe}}_2$.

Figure 1

(a) Schematic of the experimental setup showing the STM tip and an optical microscope image of the measured ${\mathrm{WSe}}_2$ on graphite sample. (b) Typical $dI/dV$ spectroscopy of monolayer and bilayer ${\mathrm{WSe}}_2$ on a log scale. (c) STM topography of a typical region of bilayer ${\mathrm{WSe}}_2$. There are two distinct defect types, with the large defects far less prevalent than the small defects. The scale bar is 20 nm. Inset: Atomic resolution of a small defect. The scale bar is 2 nm.

Figure 2

$dI/dV$ maps at constant sample biases of (a) $-1.35\mathrm{V}$ and (b) $-1.5\mathrm{V}$ on bilayer ${\mathrm{WSe}}_2$ taken over the same area as Fig. 1. The two species of defects (large and small) are easily distinguishable. The small defects additionally appear either strong or weak, depending on whether they are in the top or bottom layer. Friedel oscillations surround the defects, and their wavelength grows shorter as the energy moves deeper into the valence band. Scale bar is 20 nm for both. Insets: Fourier transforms of the maps. As the scattering wavelength grows shorter, the size of the scattering disk in momentum space grows larger. Scale bar is $3{\mathrm{nm}}^{-1}$ for both.

Figure 3

Band structure of (a) monolayer and (b) bilayer ${\mathrm{WSe}}_2$. The solid red lines are ab initio calculations of the band structure. The calculated band gap is manually set to match the spectroscopy as described in the main text. Blue dots are the experimentally extracted momentum. Points are assigned to bands as described in the Supplemental Material [26]. All points have an uncertainty in momentum of less than 10% of their preoffset value (and typically less than 5%), arising from the uncertainty in identifying the size of the scattering disk in the Fourier transforms. There is an energy smearing between 5 and 20 mV on all points due to the ac voltage added to acquire the $dI/dV$ signal. These have been omitted for clarity.

Figure 4

(a) General schematic of the conduction band of monolayer and bilayer ${\mathrm{WSe}}_2$. The relative sizes of the bands depends on the layer number. In bilayer ${\mathrm{WSe}}_2$ only the $Q$-point bands are present at the very bottom of the conduction band, and the $K$-point bands are spin degenerate. The green denotes spin-up bands and the pink denotes spin-down. (b) Simulated JDOS of the band structure shown in (a). Only the $Q$-point bands are considered. Scattering resonances shown in white are always allowed, but colored features are only possible with no spin texture on the bands. (c) Experimental FT STS on monolayer ${\mathrm{WSe}}_2$ at $V_s=+1.5\mathrm{V}$. The sharp resonances in a hexagon around the outside of the image are due to the atomic lattice. Only scattering allowed with the spin-textured bands is present (white features), implying the anticipated spin texture of the $Q$-point bands. (d) Experimental FT STS on bilayer ${\mathrm{WSe}}_2$ at $V_s=+1.3\mathrm{V}$. The same subset of scattering features allowed in monolayer ${\mathrm{WSe}}_2$ are observed, indicating strong layer polarization in bilayer ${\mathrm{WSe}}_2$. (e) Schematic of the band structure of monolayer ${\mathrm{WSe}}_2$ between the spin-split valence bands. (f) Simulated JDOS of the band structure shown in (e). (g) Experimental FT STS on monolayer ${\mathrm{WSe}}_2$ at $V_s=-1.6\mathrm{V}$. No intervalley scattering resonances are observed [blue features in (f)], implying the anticipated spin texture of the $K$-point bands. (h) Experimental FT STS on bilayer ${\mathrm{WSe}}_2$ at $V_s=-2.0\mathrm{V}$. The intervalley scattering is also suppressed, similarly indicating strong layer polarization in bilayer ${\mathrm{WSe}}_2$. The scale bars are $10{\mathrm{nm}}^{-1}$ for all, and the white hexagons represent the first BZ.