Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides

Hualing Zeng, Gui-Bin Liu, Junfeng Dai, Yajun Yan, Bairen Zhu, Ruicong He, Lu Xie, Shijie Xu,Xianhui Chen, Wang Yao, Xiaodong Cui

Supplementary Information

1. Experimental method

The measurements of the PL spectrum were carried out through a confocal-like microscopic set-up coupling to a spectrometer equipped with a CCD camera under ambient conditions. Raman spectroscopic was recorded through the Confocal Raman Microscope .The laser line 514.5 nm from the Argon laser was chosen as the exciting light source for both PL and Raman spectrum measurements. The laser beam was focused onto the sample with a spot size around 1 µm2 at a low power around 65 µW to avoid the thermal effect. The second order optical nonlinearity was investigated via the confocal laser scanning microscope with a tunable femtosecond laser system.

2. Sample Growth

Single crystals of WS2 and WSe2 have been grown by chemical vapour transport technique using iodine as transporting agent. In a first step, polycrystalline WS2 and WSe2 powders were synthesized at 1073 K for two days frommetallic tungsten, sulfuror selenium in a molar ratio of 1:2 in evacuated quartz tubes.In the second step, 1.5g of the polycrystalline WS2 or WSe2 powders and I2granule (3 mg/cc) were introduced into quartz tubes of 25 cm long. The quartz tubes were then evacuated to a pressure of about 10-5 torr and sealed.

Tubes were placed coaxially andhorizontally in a three-zone furnace with powders in the region of the hottestzone of thefurnace. The temperatures of the three zones for crystal growth were 1030 0C, 980 0Cand 930 0C, respectively. The tubes were kept in this temperature gradient of the furnacefor 10 days. At the end of this period the furnace was allowed to cool slowly at the rate of 50 0C/h to room temperature. Large shining single crystals of WS2 and WSe2were obtained bythis technique.Figure 1(a) shows the single crystal x-ray diffraction patterns of obtained WS2 and WSe2 single crystals,only (00l) peaks are observed, indicating that the single crystals are in perfect (001) orientation. In figure 1(b), the FWHM of WSe2inthe rocking curve of the (002) peak is about 0.2 degree,which indicates the single crystals are of high quality. The lattice parameters of c-direction obtained from the single crystal x-ray diffraction patterns are 12.36 Å and 12.96 Å for WS2 and WSe2, respectively, which are in consistent with literature reported before.

Figure S1: (a) X-ray diffraction pattern ofsingle crystals for WS2 and WSe2. (b) Rocking curve of (002) reflectionpeak of WSe2.

3.Ab initio results on electron density distributions of the valence band Bloch states at K points for WS2 bilayer

For WS2 bilayer, we examine the spin polarization and the electron density distribution for the four valence band Bloch states at K point (labeled as respectively, c.f. Figure S2).Each state is a spinor .The ab initio electron density are integrated either in top layer (TL) or bottom layer (BL)to get the overallpopulation in each layer for the spin up and spin down component respectively:

.

The results are given in Table S1 and they show that each valence state is highly localized in an individual layer and highly spin polarized.

Energy (eV) / 0 / 0 / -0.431 / -0.431
/ 97.96% / 0.02% / 0.62% / 1.85%
/ 1.96% / 0.07% / 0.02% / 97.43%
/ 0.07% / 2.03% / 97.22% / 0.02%
/ 0.02% / 97.88% / 2.14% / 0.07%

Table S1. Ab initio calculated electron population distribution in WS2 bilayer for the 4 valence band Bloch states at K point. denotes the population of spin component in layer L.

4. Band structure for WSe2

Besides WS2, we also calculated the band structuresfor WSe2ultrathin layers, shown in Figure S2, which are similar to the bands of WS2 ultrathin layers.

Figure S2: Ab initio calculated band structures for WSe2ultrathin layers. (a)~(d): SOC is not included; (e)~(h): SOC is included and valence band splittings at K point are shown in unit eV.