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 from metallic
tungsten, sulfur or 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 I2 granule (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 and horizontally in a three-zone furnace with powders
in the region of the hottest zone of the furnace. The temperatures of the three zones for
crystal growth were 1030 0C, 980 0C and 930 0C, respectively. The tubes were kept in this
temperature gradient of the furnace for 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 WSe2 were obtained by this 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 WSe2 in the 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 of single crystals for WS2 and WSe2. (b)
Rocking curve of (002) reflection peak 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
 (r) 
y1 , y2 , y3 , y4 respectively, c.f. Figure S2). Each state is a spinor  n   n  .
 n (r) 
The ab initio electron density are integrated either in top layer (TL) or bottom layer (BL) to
get the overall population in each layer for the spin up and spin down component
respectively:
px L =
1
yn yn
ò | y x (r) |
2
n
dr,
(x =-,¯; L = TL, BL) .
L
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.
1
2
3
4
p-TL
0
97.96 %
0
0.02 %
-0.431
0.62 %
-0.431
1.85 %
p-BL
1.96 %
0.07 %
0.02 %
97.43 %
p¯TL
0.07 %
2.03 %
97.22 %
0.02 %
p¯BL
0.02 %
97.88 %
2.14 %
0.07 %
Energy (eV)
Table S1. Ab initio calculated electron population distribution in WS2 bilayer for the 4
valence band Bloch states at K point. px L denotes the population of spin x component in
layer L.
4. Band structure for WSe2
Besides WS2, we also calculated the band structures for WSe2 ultrathin layers, shown in
Figure S2, which are similar to the bands of WS2 ultrathin layers.
Figure S2: Ab initio calculated band structures for WSe2 ultrathin layers. (a)~ (d): SOC is
not included; (e)~(h): SOC is included and valence band splittings at K point are shown in
unit eV.