Selective probing of hidden spin-polarized states in inversion-symmetric bulk MoS2

1.6 MB·

by  E. Razzoli

Selective probing of hidden spin-polarized states in inversion-symmetric bulk MoS
2
E. Razzoli,1,∗ T. Jaouen,1 M.-L. Mottas,1 B. Hildebrand,1 G. Monney,1 A. Pisoni,2 S. Muff,3,4 M. Fanciulli,3,4
N. C. Plumb,3 V. A. Rogalev,3 V. N. Strocov,3 J. Mesot,3,4 M. Shi,3 J. H. Dil,3,4 H. Beck,1 and P. Aebi1
1D´epartement de Physique and Fribourg Center for Nanomaterials,
Universit´e de Fribourg, CH-1700 Fribourg, Switzerland
2Laboratory of Physics of Complex Matter, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland
3Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
4Institute of Physics, E´cole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland
(Dated: January 26, 2017)
Spin-andangle-resolvedphotoemissionspectroscopyisusedtorevealthatalargespinpolarization
7
is observable in the bulk centrosymmetric transition metal dichalcogenide MoS . It is found that
1 2
the measured spin polarization can be reversed by changing the handedness of incident circularly-
0
polarizedlight. Calculationsbasedonathree-stepmodelofphotoemissionshowthatthevalleyand
2
layer-lockedspin-polarizedelectronicstatescanbeselectivelyaddressedbycircularly-polarizedlight,

n thereforeprovidinganovelroutetoprobethesehiddenspin-polarizedstatesininversion-symmetric
a systems as predicted by Zhang et al. [Nature Physics 10, 387 (2014)].
J

4
2 Transition metal dichalcogenide (TMDC) monolayers izationontheS-Mo-Slayersofthe2H-stackedMoS unit
2

have been heavily investigated due to the locking of cell. Our findings not only highlight the locking of the
]
i the spin with valley pseudospins and the presence of spin with layer and valley pseudospins in MoS but also
c 2
a direct gap, which makes them ideal candidates for provide a novel and improved route, other than taking
s
- valleytronic devices [1]. Thanks to the lack of inver- profit of the inelastic mean free path (IMFP) [8], for se-
l
r sion symmetry and the non-negligible spin-orbit cou- lectivelyprobinghiddenspin-polarizedbandsininversion
t
m pling, TMDC monolayers also feature well-defined spin- symmetric systems.
. polarized ground states [2], which can in principle be The soft x-ray ARPES and spin-ARPES experiments
t
a investigated by spin- and angle-resolved photoemission were respectively performed at the ADRESS beamline
m spectroscopy(spin-ARPES).However,whilefewARPES [10] and at the COPHEE end-station of SIS beamline at
- studies clearly observed the indirect to direct band gap the Swiss Light Source, Paul Scherrer Institut, Villigen,
d
transition going from the bulk crystal to the monolayer Switzerland. Base pressures were better than 4×10−10
n
[3–6],spin-ARPESinvestigationofTMDCmonolayersis mbar, with a sample temperature of ∼25 K [11]. The
o
c more challenging, given the low cross-section of photoe- chemical vapor transport-grown 2H-MoS2 crystal con-
[ mission from single layers. sisting of hexagonal 2H-stacked S-Mo-S layers separated

ARPES measurements on the bulk system are instead byavanderWaalsgap(Fig. 1(a)[18]),hasbeencleaved
1
v less demanding but early studies detected spin-resolved in-situ at low temperature. Figure 1(b) (top panel)
9 signals only from TMDCs with broken inversion sym- shows the ARPES intensity plot of bulk MoS along the
2
0 metry [7]. Interestingly, a recent theoretical study [8] K-Γ high-symmetry direction of the Brillouin zone [bot-
1
suggested that the spin texture of the TMDC could be tomofFig. 1(a)]andmeasuredusingcircularly-polarized
7
probed by photoemission, even in the inversion symmet- lightwithanoverallenergyresolutionof50-80meV.The
0
. ric bulk TMDC crystals, as a result of the localization of observed bands are in agreement with previous ARPES
1
two spin-degenerated valence band maxima on different measurements[3,5,20],withthetopofthevalenceband
0
7 layers of the unit cell and of the finite penetration depth at Γ originating from Mo dz2/pz orbitals and that lies
1 of the photoemission process probing preferentially the ∼600 and ∼800 meV above the upper (VB1) and lower
: uppermostlayer. Experimentallythiseffecthasbeenob- (VB2) valence bands at K with mainly Mo d , d
v x2−y2 xy
i served for WSe2 where the spin orbit (SO) coupling is orbital characters. The observed dispersion is in good
X
the strongest one among the TMDCs [9]. agreementwithourdensityfunctionaltheory(DFT)cal-
r Here we show that a large out-of-plane spin- culation within the local density approximation (LDA)
a
polarization is observable in the bulk dichalcogenide between Γ and K, given the small kz−dispersion along
MoS ,andmoreimportantly,thatitssigndependsonthe K−H direction (see Fig. 1(b) bottom panel) [11].
2
handednessoftheincidentcircularly-polarizedlight. Our Figures1(c)-(e)presenttheexperimentalspin-ARPES
calculations, based on a three step model of the photoe- intensities (top) and the spin-polarization energy distri-
mission process demonstrate that the observed spin re- bution curves (bottom) at the K point along the three
versalisaninitialstateeffect. Usingleft(C )andright- spatial coordinates x, y, and z in the sample frame mea-
L
handed(C )circularly-polarizedlightresultsinselecting suring in-plane (P , P ), and out-of-plane (P ) spin po-
R x y z
different initial states that present a positive or negative larization. Conversion from the coordinate system given
out-of-plane spin polarization depending on their local- by the Mott polarimeters to the sample frame is per-
2
FIG.1: (a)Structuralmodel(top)andBrillouinzone(bottom)of2H-MoS . (b)ARPESintensitymapalongK−Γdirection
2
(top), and DFT-LDA calculated band structure showing the band dispersion along K −Γ and H −K directions (bottom).
(c)-(d) Spin-resolved intensities (top) and spin polarization curves (bottom) at the K-point along x, y, and z, respectively.
ContinuousredlinesinthebottompanelsareGaussianfits,resultinginP =∓0.08,P =±0.05andP =∓0.28. Spin-ARPES
x y z
data were acquired at hν =50 eV with s−polarized light.
formed according to [19]. The difference in binding en- inducedterminthelight-matterinteractionHamiltonian
ergy between VB1 and VB2 is 170 meV, in agreement Hint [25]isresponsibleforthespineventstunedbylight
SO
with previous studies [20]. The measured spin polariza- polarization. However, in contrast to the TI that exhibit
tionisalmostentirelyout-of-planewithanegligiblesmall extremely large SO-coupling, in TMDCs and especially
in-planecomponent. Themeasuredout-of-planespinpo- inMoS [5],the(cid:104)i|Hint|f(cid:105)termcanbeneglectedandthe
2 SO
larization points upwards and downwards for the upper observed flip in the out-of-plane spin-polarization has to
and lower valence band, respectively, similarly to what be related to a different mechanism [11].
has been observed in WSe [9]. Instead, the origin of the sign inversion of P can be
2 z
understood analyzing the idealized case of a TMDC bi-
The z-component of the spin polarization displays an
layerwithsmallinterlayercouplingt . Inthissimplified
interesting polarization dependence [Fig. 2]. The spin ⊥
model, the top of the valence band VB1 (E = E ) at
polarization measured with p- [Fig. 2 (a)], and C po- b 1
L
K isdoublydegenerateandoriginatesinMod , d
larization [Fig. 2 (b)] are in agreement with the obser- x2−y2 xy
orbitals. The eigenstates expressed in terms of spherical
vation with s-polarized light [Fig. 1 (e)], with the only
harmonics |l,m(cid:105) are then given by [11, 26]:
difference of an increasing absolute value of the spin po- µ
larization fraction. Instead, when probed with C light
R cosα|2,2(cid:105) +sinα|2,−2(cid:105)
the out-of-plane spin polarization changes its sign, i.e., |1,E1(cid:105)= 1 √ 2 |↑(cid:105)
2
the z-component of the detected photo-electron points (1)
sinα|2,2(cid:105) +cosα|2,−2(cid:105)
upwardsanddownwardsfortheloweranduppervalence |2,E (cid:105)= 1 √ 2 |↓(cid:105)
1
band, respectively [Fig. 2 (c)]. Interestingly, the light 2
handedness-induced reversal of the z-component is also
usingµ=1(2)fortheupper(lower)Molayerofthe2H-
observable at other photon-energy [e.g. at hν = 58 eV
stacked MoS unit cell [Fig. 3(a)], and with cos2α =
2
as shown in Fig. 2 (d)-(e)], therefore indicating that it (cid:112)
λ / λ2 +t2 that corresponds to the spin-dependent
does not depend on the three-dimensional (k ) band dis- so so ⊥
z layer polarization of the holes states. The spin-valley
persion.
coupling of holes in monolayers λ is calculated to be
so
A possible explanation of our observation would be 1.7 times higher than the interlayer hopping t in MoS
⊥ 2
that photoelectron spin flips during the photoemission [26], therefore resulting in a substantial layer-dependent
process, i.e., we observed a final state matrix element spin-polarization (cos2α=0.863).
effect. Up to now, most of spin-ARPES studies dealing The states |1,E (cid:105) and |2,E (cid:105) respectively contribute
1 1
with k-resolved light-induced spin rotations have been to the spin-up (I(cid:15) ) and spin-down (I(cid:15) ) intensity [11]:
↑,z ↓,z
carriedoutontopologicalinsulators(TI),duetothelarge
strength of the SO-coupling and to the high quality of I↑(cid:15),z ∝|cos(α)κ2,2·(cid:15)+sin(α)δe−ik·dlκ2,−2·(cid:15)|2
(2)
the ARPES data in such systems [21–24]. It has been I↓(cid:15),z ∝|sin(α)κ2,2·(cid:15)+cos(α)δe−ik·dlκ2,−2·(cid:15)|2
experimentally shown that light-induced spin rotations
are observable only at low photon energy (about 6 eV) withκ =(cid:104)eik·r|r|l,m(cid:105),d =(1a,2a,−1c)therelative
l,m l 2 3 2
[21,24]. TheoreticallyithasbeensuggestedthattheSO- atomic displacement between the upper and lower Mo
3
FIG. 2: Spin-ARPES data acquired at hν =50 and hν =58 eV. (a)-(c) Spin-resolved intensities (top) and spin polarization
curves (bottom) along z at the K-point acquired with p, C and C polarization, respectively (hν = 50 eV). (d), (e) Spin-
L R
resolved intensities (top) and spin polarization curves (bottom) at the K-point acquired with C and C polarization, and
L R
hν =58 eV. Continuous red lines in the bottom panels are Gaussian fits, resulting in P (p,50 eV)=∓0.50, P (C ,50 eV)=
z z L
∓0.68, P (C ,50 eV)=±0.85, P (C ,58 eV)=∓0.54, and P (C ,58 eV)=±0.91.
z R z L z R
layers, (cid:15) the light polarization vector, and δ =e−2λce, an hidden-spin polarized state will be observed, but also
attenuationfactorthattakesintoaccountthephotoelec- overcomes the IMFP-limited probing of the spin texture
trons IMFP λ . For normal incident circularly-polarized of the uppermost layer as introduced by using linearly-
e
light the conservation of the total angular momentum polarized light [8, 9, 27, 28].
dictates that only the states with mk = m ± 1, can This interpretation is confirmed by calculating the
give a non-vanishing contribution to κl,m, once the free- spin-resolved ARPES intensity and the spin polarization
electronfinalstateisdecomposedinsphericalharmonics for 8 MoS layers as a function of both, the light geom-
|eik·r(cid:105)=(cid:80)lk,mkdlk,mk(k,r)|lk,mk(cid:105). etry and p2olarization and using the spin doublet of the
In Fig. 3 we illustrate the dipole-allowed transitions topmost VB (VB1) in valley K as the initial state [11].
for the eigenstate of VB1 at the K point, for the case of The spin up (down) state is highly localized on the odd
vanishing interlayer coupling (α = 0). In this case spin
up and spin down states are fully locked on the upper
and lower S-Mo-S layer, respectively [Fig. 3(a)].
For C light [Fig. 3(b), left-hand-side], the available
L
final states have m = m − 1, and are {|1,1(cid:105),|3,1(cid:105)}
k
for m = 2 and {|3,−3(cid:105)} for m = −2. As expected
from the higher number of final states available for a
dipole transition from a state with m=2, our numerical
evaluation shows that the cross-section for transition to
the states {|1,1(cid:105),|3,1(cid:105)} is one order of magnitude larger
than to {|3,−3(cid:105)}, i.e., |κ ·(cid:15)n |/|κ ·(cid:15)n |≈10 [11].
2,2 CL 2,−2 CL
Similarly and according to the relation κ ·(cid:15) =
l,±m CR/L
κ ·(cid:15) , the available final states of a dipole tran-
l,∓m CL/R
sition induced by C light [Fig. 3(b) right-hand-side],
R
have m =m+1 and |κ ·(cid:15)n |/|κ ·(cid:15)n |≈10. For
k 2,−2 CR 2,2 CR
a non-zero interlayer hopping, eq. (2) thus gives:
(cid:15)n (cid:15)n
PCRn/L = I↑,CzR/L −I↓,CzR/L ≈∓cos2α. (3)
z (cid:15)n (cid:15)n
I CR/L +I CR/L
↑,z ↓,z
This demonstrates that the layer-locked, hidden spin- FIG. 3: (a) Schematic of the layer-resolved band dispersion
polarized states of the K valley can be probed through of VB1 and VB2 around the K point. (b) Dipole-allowed
the spin-dependent selection rules introduced by the use transitions for the eigenstate of VB1 for vanishing interlayer
coupling (α=0) at the K point.
of circularly-polarized light. This not only selects which
4
FIG. 4: Three-step model photoemission calculations. (a)-(d) Spin polarization (P ) maps for p, s, C and C polarization,
z L R
respectively(hν =50eV).(e)Experimentalandsimulatedspinpolarizationalongz. (f)-(h)radialintegral(ρ),photonenergy
(hν) and IMFP (λ )-dependence of P , respectively. Empty symbols in (g) show the experimental P from Fig. 2 (a)-(e).
e z z
(i)-(n) Spin-resolved intensity maps for C (top panels) and C (bottom panels) polarized light.
L R
(even) Mo layer, in analogy to the bilayer model and λ , the possible light geometries. As the result of the finite
e
includedfollowingthemethodsproposedby[22,23], has λ at hν = 50 eV, they also show higher ARPES inten-
e
been fixed to the interlayer distance (6.1 ˚A). sities for C than for C [Fig. 4 (i), (n) and (l), (m)],
L R
The spin polarization intensity maps as a function of with a theoretical I↑(C )/I↓(C ) ratio of 2.65, in close
L R
the incoming light geometry and polarization [Fig. 4 agreement with the experimental value of 2.1 [30].
(a)-(d)] [29], show that for s− and p-polarized light the We finally note that putative interference effects be-
z-component of the spin is positive irrespective of the tween distinct degenerate initial states [31] and/or small
geometry, in agreement with our experimental observa- correction to eq.(1), resulting from possible modification
tions and with what is expected in MoS as the result within the MoS monolayer, such as mirror symmetry
2 2
of the finite probing depth of the photoemission process breaking and VB1-VB2 intervalence mixing, might con-
[8, 9]. Our model further predicts positive and negative tribute to the spin-polarization. In bulk TMDCs, these
spinpolarizationforC andC -polarizedlightsformost contributions only slightly change P but may substan-
L R z
of the possible experimental geometries, including ours tiallyaffectthein-planespin-polarization(P )[11]. Sim-
(cid:107)
(θ =48.3◦ andφ =71◦), aswellassigninversionfor ilar to previous studies [9], we observe a small P [Fig. 1
ph ph (cid:107)
extremegeometriescorrespondingtograzingincidenceof (c)-(d)], which becomes more sizeable with other polar-
the radiation [Fig. 4 (c), (d)]. ization [11]. For supported TMDC layers the interaction
Overall,thetheoreticalP valuesobtainedforthevari- with the substrate may in some cases enhance these ef-
z
ouslightpolarizationandcorrespondingtoourgeometry fects whose contributions to both P and P might be-
z (cid:107)
agree well with the experimental data as shown in Fig. come more important [32].
4 (e). The weak dependence of the spin-polarization on In conclusion our ARPES and spin-ARPES measure-
the radial integral of the overlap between the initial and mentsofbulkcentrosymmetric2H-MoS haverevealeda
2
the final state (ρ) indicates that the calculations are not large out-of-plane spin-polarization with sign depending
stronglydependentonthenumericaldetailsofthechosen on the handedness of incident circularly-polarized light.
states [Fig. 4 (f)], and the observed spin-flip is predicted Ourcalculations,basedonathree-stepmodelofthepho-
to be robust against changes in the photon energy [Fig. toemission process demonstrate that this relates to an
4 (g)], as experimentally observed [Fig. 2 (b)-(e)]. The initial-state effect of photoemission through the dipole
dependence of the calculated P on λ [Fig. 4 (h)] also selection rules that allow to intimately probe the val-
z e
confirmsthatusingcircularly-polarizedlightallowsover- ley and layer spin texture of the electronic states. Our
coming the IMFP limitation in variance with the case of finding provides a novel route for studying hidden spin-
linearly polarized lights where a presence of a small λ polarized bands of inversion symmetric systems in laser-
e
is essential for observing any spin polarization. Finally, or soft x-ray-ARPES where the inelastic mean free path
thespin-resolvedintensitymapsinFig. 4(i)-(n)account of photoelectrons is typically large.
fortheselectiveabilityofthecircularly-polarizedlightto We acknowledge F. Boschini, M. Michiardi and A.
probe the layer-locked spin-polarized states for most of Damascelli for valuable discussions. This project
5
was supported by the Fonds National Suisse pour la J. Synchrotron Rad. 21 (2014) 32.
Recherche Scientifique through Div. II. E.R. acknowl- [11] See Supplemental Material [url], which includes Refs.
edges support from the Swiss National Science Founda- [12–17]
[12] A.Kuc,N.Zibouche,andT.Heine,Influenceofquantum
tion (SNSF) grant no. P300P2 164649.
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polarization in centrosymmetric MoS2 bulk crystals Sci- electronspinpolarizationinangle-resolvedphotoemission
entific Reports 6, 26197 (2016). frombothatomicandcondensedmattertargets,J.Phys.:
[28] Forthecaseofnormalincidentlinearly-polarizedlightall Condens. Matter 24 173001, (2012).
states with mk −m = 0,±1 are equally accessible, this [32] S.-K. Mo, C. Hwang, Y. Zhang, M. Fanciulli, S. Muff,
result in |κ2,−2·(cid:15)p/s|≈|κ2,2·(cid:15)p/s|, and a positive spin J. H. Dil, Z.-X. Shen, and Z. Hussain Spin-resolved pho-
polarization is observable only when a disproportion of toemssion study of epitaxially grown MoSe and WSe
2 2
intensity from the two initial states is introduced by the thin films,J.Phys.: Condens.Matter28,454001(2016).
IMFP.
[29] The P maps have been calculated according to the for-
z