Photoinduced valley-polarized current of layered MoS2 by electric tuning

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by  Yunjin Yu

Photoinduced valley polarized current of layered MoS by electric tuning
2
Yunjin Yu,1 Yanfeng Zhou,2 Langhui Wan,1 Bin Wang,1 Fuming Xu,1 Yadong Wei,1, and Jian Wang3,
∗ †
1College of Physics Science and Technology, and Institute of Computational Condensed Matter Physics,
Shenzhen University, Shenzhen 518060, P. R. China
2International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, P. R. China
3Department of Physics, The University of Hong Kong, Hong Kong, P. R. China
(Dated: January 9, 2017)
7
1 PhotoinducedcurrentoflayeredMoS2 basedtransistorisstudiedfromfirstprinciples. Underthe
0 illumination ofcircular polarized light, valley polarized currentis generated which can betunedby
2 the gate voltage. For monolayer MoS2, the valley polarized spin up (down) electron current at K
(K′) points is induced by the right (left) circular polarized light. The valley polarization is found
an toreach+1.0(-1.0) forvalleycurrentthatcarriedsuchaK (K′)index. ForbilayerMoS2,thespin
up (down) current can be induced at both K and K′ valleys by the right (left) circular light. In
J
contrasttomonolayerMoS2,thephotoinducedvalleypolarizationshowsasymmetricbehaviorupon
6
reversal of the gate voltage. Our results show that the valley polarization of photoinduced current

can be modulated by the circular polarized light and the gate voltage. All the results can be well
]
l understood using a simple K·P model.
l
a
h
- As one ofthe mostpromisingtwo-dimensionalmateri- and conduction band both spin-dependent and valley-
s
als, graphene has shown exceptional physical, chemical, dependent. Carriers with various combinations of val-
e
m and optical properties.[1–4] However, pristine graphene ley and spin indices can be selectively excited by optical
doesn’t have gap between valence band and conduc- fields with different circular polarizations.[19, 20] Circu-
.
t tionbandwhichhampersitsapplicationsinsemiconduc- larlypolarizedluminescence has been observedin mono-
a
m tor devices. Although layered transition-metal dichalco- layer MoS2 and bilayer MoS2 under circularly optical
genide (TMDC) has the similar hexagonalstructure like pumpingwithdifferentfrequencies.[21,22]Thisconfirms
-
d graphene, it shows distinctly different properties from the theoretical prediction that the circular polarization
n graphene.[5–8] Firstly, TMDC has strongspin-orbitcou- originatesfrom the contrastingselectionrules for optical
o plingwhichisoriginatedfromthed orbitalsoftheheavy transitions in different valleys[19].
c
metal atoms. This makes TMDC an exciting platform Forthe potentialdeviceapplicationoflayeredTMDC,
[
toexplorespintronicapplications.[9–11]Secondly,mono- the key issue is to examine the performance of nanoelec-

1 layerTMDC,duetoitsinversionsymmetrybreaking,dis- tronic devices such as transistors. Indeed, the proper-
v plays distinct physical properties from its bulk counter- ties of electron-hole transport and photovoltaic effect in
0
part. TMDC crossoversfroman indirectband gapsemi- gatedMoS Schottkyjunctionwerestudied.[23]Thepho-
2 2
5 conductoratbulk toadirectbandgapsemiconductorat totransistor based on monolayer MoS2 exhibited good
1 monolayer.[12, 13] Most importantly, monolayer TMDC photoresponsivity and prompt photoswitching, and the
0 has six valleys at the corners of its hexagonal Brillouin mechanism of photoresponse was analyzed in the ultra-
. zone,whichcanbeclassifiedintotwoinequivalentgroups. thin MoS field-effect transistors by scanning photoin-
1 2
0 Such valleys have large separations in momentum space duced current microscopy.[24–27] So far, most of the in-
7 whichmakesthe valley index robustagainstsmalldefor- vestigations concentrate on the I-V characteristics and
1 mation of its lattice and low-energy scattering by long less attention has been paid on the valley information.
: wavelength phonon. This means that the valley index Since one of the major challenges in valleytronics is the
v
i can be used as a potential information carrier. The val- generation of valley polarized current, it is important to
X ley properties of graphene has been extensively studied studythevalleypolarizedcurrentthroughlayeredMoS .
2
r theoretically.[14–16] Recently, there has been a growing In this letter, we investigate the properties of valley po-
a
interestinthespecialspinandvalleypropertiesoflayered larizedcurrentoflayeredMoS phototransistorfromfirst
2
TMDC both experimentally and theoretically.[17, 18] principles and analyze our results using K·P model.
Xiaoet al[17]foundthatinmonolayerTMDC,inversion
In this work,we calculate the photoinduced valley po-
symmetrybreakingandspinorbitcoupling(SOC)leadto
larizedcurrentinmonolayerandbilayerMoS phototran-
2
coupled spin and valley physics. Monolayer TMDC has
sistors. As shown in Fig.1, the phototransistor consists
opposite spins at the two inequivalent K points, mak-
of two semi-infinite sheets of monolayer/bilayerMoS as
2
ing the optical transition rules between valence band
leads and a central scattering region. A vertical electric
fieldEalongz directionisproducedbyapplyingthegate
voltage V at the bottom gate in the central scattering
g
region. In the numerical calculation, the sizes of super-
∗Electronicaddress: [email protected]
cellsusedinourcalculationaresettobe10.34a ×47.77
†Electronicaddress: [email protected] B
a × 40.0 a for monolayer MoS and 10.34 a × 47.77
B B 2 B
2
a × 55.0 a for bilayer MoS . The band gaps we get
B B 2
here are Emono = 1.7534 eV for monolayer MoS and
gap 2
Ebi =1.7278 eV for bilayer MoS , which are similar to
gap 2
those of reference 28 andreference 29, althoughthey are
under estimated comparing to the experimental results
of reference [12]. We will focus on the transport along
armchair direction when the circularly polarized light is
shined on the central region. An external bias voltage
V = 0.3 V is applied across the central region in or-
b
der to collectvalleypolarizedphoto current. The energy
of incident light is assumed to be equal to the direct en-
ergygapEmono formonolayerMoS andEbi forbilayer
gap 2 gap
MoS , respectively.
2
To calculate the photoinduced current of such de-
vices, we treat electron-photon coupling as a pertur-
bation on the self consistent Hamiltonian of electronic
degrees of freedom H .[30–32] To obtain the nonequi- FIG. 1: Schematic plots of monolayer (upper) and bilayer
e
librium Hamiltonian H of open structures, we em- (lower)MoS2phototransistors. Eachcentralscatteringregion
e
ploy the state-of-the-art first principles method based controlledbythegatevoltageVg issandwichedbysourceand
drain regions that extend to y =∓∞. The energy of shining
on the combination of density functional theory and
light is expressed in terms of ~ω.
the Keldysh nonequilibrium Green’s function formalism
(NEGF-DFT).[33] The system nonequilibrium Hamilto-

nian H is self-consistently determined through NEGF-
e 30 (a) 30 (b)
DFT calculation which includes spin-orbital coupling 25 25
(lciSugOrhrtIe)nc,toenxdsteiensrtsnsitayolfbfuibanoscthtviooelntlaecgthtereiaocnrydang(dCatDmeFavTgonl)teatmgicea.yfiSebilndecse,mttohhreee 2 m/photon) 1125050 ffffkkkk,,’’,, 1120505 ffffkkkk,,’’,,
afipelpdrosptrreiantgethtoasdiessctrhiebecatsheeinphthoitsocpuarpreern,tD.[3F4T] Fmoarysmbealal se (n -01.0 -0.5 0. 0 0.5 1.0 -01.0 -0.5 0 .0 0.5 1.0
n
good approximation. po 30 (c) 30 (d)
paOckuargceaNlcaunloaDtioCnawl.[a3s5p,3re6f]oDrmouebdlue-sζinbgatshisesfiertswtapsriunsceipdlteos otores 2205 ffkk,, 22 05 ffkk,,
expand the wave functions and the exchange-correlation Ph 1105 ffkk’’,, 1105 ffkk’’,,
potentialwastreatedatlocalspindensityapproximation 5 5
(LSDA) level.[37–40] The mesh cut-off energy was set -01.0 -0.5 0.0 0.5 1.0 -01.0 -0.5 0.0 0.5 1.0
to be 200 Ry and numerical tolerance of self-consistency
Vg (V)
was restricted to 10 4 eV. To consider the k-sampling,
−
FIG. 2: The valley and spin components of photoresponse of
mesh 12×1×1 in k-space is used. After obtaining H ,
e
monolayer(panel(a)and(b))andbilayer(panel(c)and(d))
we treated the electron-photoninteractionH by the
first order Born approximation. Here, He phe=−phmeA·P, McoorrSe2spboynadbtointihtieocmaseethoofdri.ghTthceirlceuftlatrwpooplaarnizeelsd(l(igah)taσn+d,(tch)e)
where A is the electromagnetic vector po−tential and P
right two panels ((b) and (d)) correspond to the case of left
the momentum of the electron. Detailed procedures of circular polarized light σ−.
obtaining Green’s function have been discussed in refer-
ence 41.
The photoinduced valley and spin dependent current where, f is the Fermi distribution function of lead α,
α
in the lead α can be written as[41, 42] Γ is the linewidth function which reflects the coupling
α
between lead and central scattering region, G<,> is the
ph
e dE
Iph = Tph(E,k,s). (1) Green’s function including the contribution of voltage
α,τ,s ~Z 2π α and photons.[41]
kXτ
∈ To describe the current response to the light, we ex-
Here,α = S/D stands for the lead of source/drain. τ = amine the photoresponse, which is defined as
±1 (corresponding to K/K ) is the valley index and k
′
around K or K′ is calculated starting from the point f = Iτp,hs , (3)
of K or K′, s is the spin index. Tαph is the effective τ,s eFph
transmission coefficient of lead α, and its expression is
where Iph is the current with valley index τ and spin
τ,s
Tαph(E,k,s)=Tr{iΓα(E,k)[(1−fα)G<ph+fαG>ph]}ss, index s. Fph is the photon flux defined as the number of
(2) photons per unit time per unit area.
3
polarization changes from -0.25 to 0.05 in bilayer MoS
2
(blue dot line in panel (b)) in the gate voltage window
[−1.0,1.0]V when σ+ light is shed. The valley polariza-
(a) (b)
1.0 0.2 tionprofileησ(Vg)satisfiesη+(Vg)=−η (Vg). Hencefor
bilayer MoS , the valley polarization ca−n be modulated
2
zation 0.5 0.1 bWyethalesocirficnudlatrhpaotlathriezemdoldiguhltataisonweelffleacsttohfengeagtaetivvoeltgaagtee.
polari 0.0 0. 0 voltage is more significant than that of positive one. To
y explainallofthesephenomena,weexaminethefollowing
e
all K·P model.
V -0.5 -0.1
Due to the inversionsymmetry breaking andthe pres-
ence of strong spin-orbit coupling in monolayer MoS ,
-1.0 -0.2 2
spin and valley degrees of freedom couple to each to-
gether, i.e, K (K ) valley is occupied by the spin-up
′
-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0
(down) electrons at the top of the valence band. The
Vg (V) electron interband transition from the top of spin-split
valence band to the bottom of the conduction band can
FIG. 3: The valley polarization versus gate voltage in mono-
beinducedbythecircularpolarizedlightσ . Ifwedefine
lmayeethro(dp.anTelhe(ab))luaenddobtillainyeerco(prraenseplo(bn)d)sMtooSth2ebcyasaeboifniσti+o thecouplingstrengthwithσ± opticalfields±asP (k,sz),
lightandthereddotlinecorrespondstothecaseofσ− light. we have the following coupling intensity for tra±nsitions
near K/K points[17]
′
ξ
Figure 2 shows the valley and spin polarized photore- |P (k,τ,s )|2 =|P |2(1±τ ′ ), (5)
z 0
sponse versusgate voltageunder bias voltage0.3V.The ± ξ′2+4a2t2k2
solidredline,solidblueline,dashedredline,anddashed where |P |2 = m20a2t2, ξ = ξp− τs λ, m is the free
blue line correspond to photoresponse fK, , fK, , fK′, , 0 ~2 ′ z 0
and fK′, , respectively. From panel (a), w↑e see t↓hat th↑e electron mass, a is the lattice constant, t is the effective
compone↓ntf ,isatleastoneorderofmagnitudelarger hoppingintegral,ξistheenergygap,τ =±1isthevalley
K,
than other thr↑ee components, indicating that the right index, 2λ is the spin splitting at the top of valence band
circular polarized light σ+ mainly excites the spin-up caused by SOC, and sz is for spin. To characterize the
polarization of coupling, we define
electrons at K point from the valence band to the con-
duction band in monolayerMoS2. Similarly we conclude |P (K)|2−|P (K )|2
fmroaminlfiyguexrecit2e(sb)ththeastptihne-dloewftncierlceucltarronpsolaatrizKed lpigohinttσi−n η±c = |P±(K)|2+|P±(K′′)|2. (6)
′ ± ±
mmoetnroylabyreerakMinogS2in. mTohnisolpahyeenroMmoeSnoannidscdaunebteoetxhpelasiynmed- Here, |P±(K/K′)|2 = sz=±12 |P±(K/K′,sz)|2. Since k
2 is very small near K Por K points, we have ξ ≫ atk.
′ ′
byopticalselectionrule.[17]Thesituationisdifferentfor This in turn gives ηc = ±1 from Eq. (6). The behavior
bilayer MoS2 where the inversion symmetry is restored. ofpolarizationofcou±plingintensityisalmostthesameas
In this case, the spin up components of photonresponse that of valley current polarization obtained from ab ini-
(fK, andfK′, )aremuchlargerthantheothertwocom- tio calculation shown in figure 3(a). This suggests that
pone↑nts when↑σ+ light is shed (panel(c)), whereas the
the polarizationof valley current calculated from ab ini-
spindowncomponents(fK, andfK′, )dominateforσ− tio method is intimately related to the polarization of
light (panel(d)). ↓ ↓
coupling from the K·P model in monolayer MoS .
2
Tocharacterizevalleyinjection,wedefinevalleypolar-
The situationis morecomplicated in bilayerMoS . In
2
ization η as
this paper, we consider AB stacked bilayer MoS which
2
maintainstheinversionsymmetry. Tomimictheeffectof
η = IKph−IKph′ (4) the gate voltagein ab initio calculation, we introduce an
IKph+IKph′ electric field along z direction in our K·P model Hamil-
tonian. The K·P model Hamiltonian for bilayer MoS
2
where Iph = Iph +Iph. From the panel (a) of figure 3, with perpendicular external electric field is expressed as
K K K
weseethatalmo↑stfully↓polarizedvalleycurrentisgener- follows:[43]
atedusingeitherσ+orσ incidentlight. Inaddition,the
vovaafllllgeeayyteppoovlloaalrrtiiazzgaaettsiioofnnrsoomrfemm-1oa−.ni0nolVcaoynteorstMa1n.0otSVi2n,itsshureogbgweuhssottilneaggraatinhngasett H(k,τ,sz)=at(τξ−kx00∆−2Uiky)a−tτ(τskztxλ0⊥+−i∆k2yU)at(τξ+kx00∆+2Uiky)aτt(sτzkλtx0⊥+−∆i2kUy).
the gate voltage. In contrast, we find that the valley (7)
polarization is very sensitive to the gate voltage for bi- where t is the intralayer hopping constant, ∆U = Ed,
layerMoS . As shownin panel (b) of figure 3, the valley E is the⊥magnitude of external electric field and d is the
2
4
distance between two monolayers. The external electric
fieldE willinduce anenergyshiftof ∆U atupper layer
−2 1.0 1.0
andanenergyshift ∆2U atlowerlayerinthebilayerMoS2. 2 )
Henecree4a3llathnedptahreambaestiesrissin{|Eduzq2.(>7),√a1r2e(|tdauxk2eny2fr>om−tihτe|druxeyfe>r- 222 mat/00.8 (a) K, 0.8 (b) K,
),|dBlzy2 d>ia,g√o12n(a|ldilxz2in−gy2E>q.+(7iτ),|dwlxeyo>b)t}a.inth−eeigenfunctions nsity (0.6 KKK,’’,, 0. 6 KKK,’’,,
e
|K ↑>, |K ↓>, |K′ ↑>, and |K′ ↓> with k= 0 near the g int0.4 0.4
top valence band as follows, plin
ou0.2 0.2
0 0 C
|K ↑>= sinα1 ⊗|↑>,|K ↓>= sinα2 ⊗|↓>,
(cid:18) 0 (cid:19) (cid:18) 0 (cid:19)
cosα1 cosα2 0.0 0.0
-0.04 -0.02 0.00 0.02 0.04 -0.04 -0.02 0.00 0.02 0.04
0 0
|K ↑>= sinα2 ⊗|↑>,|K ↓>= sinα1 ⊗|↓> (8) U (eV)
′ (cid:18) 0 (cid:19) ′ (cid:18) 0 (cid:19)
cosα2 cosα1
FIG. 4: The coupling intensity versus electron potential en-
with ergy difference∆U between the bottom and top layers of bi-
t layerMoS2. Panel(a)correspondstothecaseofσ+lightand
sinα1 = ⊥ , panel (b) corresponds to thecase of σ− light.
t2 +(E +λ+ ∆U)2
v1 2
q ⊥
E +λ+ ∆U
cosα = v1 2 ,
1
qt2⊥+(Ev1+λ+ ∆2U)2 0.4 (a) 3 (b) 0.2 (c)
csoinsαα22 == qqtt2⊥2⊥E++v((2EE+vv22tλ⊥++−λλ∆−−2U∆∆22UU))22,, (9) Coupling polarization-000...022 -1 12DOS (eV) -dified coupling polarization000...011
o
M
and -0.2
-0.4
0
∆U -0.04-0.020.000.020.04 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0
Ev1 =rt2 +(λ+ 2 )2, U ( eV) Vg (V) Vg (V)
⊥
E = t2 +(λ− ∆U)2. (10) FIG.5: (a) Thecoupling polarization versus∆U calculated
v2 r 2 from Eq. (12) of K·P model. The blue dotted line is for the
⊥
case of σ+ light, the red dotted line for the case of σ− light.
Under the illumination of circular polarized light, the
(b) DOSof upperlayer Mo atom (red dotted line) and lower
coupling intensities are found to be layerMoatom(bluedottedline)versusthegatevoltagebyab
initiomethod. (c)Themodifiedvalleypolarizationversusthe
|P (K,↑)|2 =|P |2cos2α ,|P (K,↓)|2 =|P |2cos2α ,
+ 0 1 + 0 2 gate voltage (actually ∆U) from Eq. (13). The blue dotted
|P (K,↑)|2 =|P |2sin2α ,|P (K,↓)|2 =|P |2sin2α , line corresponds to the case of σ+ light, the red dotted line
0 1 0 2
|P −(K ,↑)|2 =|P |2sin2α ,|P −(K ,↓)|2 =|P |2sin2α , to thecase of σ− light.
+ ′ 0 2 + ′ 0 1
|P (K ,↑)|2 =|P |2cos2α ,|P (K ,↓)|2 =|P |2cos2α .
′ 0 2 ′ 0 1
− −
(11)
1
Figure4showsthecouplingintensityversusthetwolayer ηc =± (cos(2α )+cos(2α )) (12)
1 2
potential energy difference ∆U in bilayer MoS2 by K·P ± 2
model. The results are similar to those of figure 2 by
In figure 5(a), we plot the valley coupling polarization
the ab initio method. Our ab initio calculation shows
versus the gate voltage using the formula above. Similar
that V = 1.0 V gives rise a potential difference 0.04
g to figure 2(b), we have ηc(∆U) = −ηc(∆U). However,
V between the top and bottom layers in bilayer MoS . +
2 we also have a relation ηc(∆U) = −η−c(−∆U), i.e., ηc
Hence we plot the coupling intensity versus ∆U from
areoddfunctionsof∆U w±hicharediffer±entfromourfirs±t
∆U =−0.04V to 0.04 V in figure 4 in order to compare
principles results. In fact, from Eq. (12) one can easily
with figure 2, where V is from -1.0 V to 1.0 V.
From Eq. (6), the vgalley coupling polarization for bi- getη±c →±(λ2+tt2⊥2⊥)3/2∆U when∆U →0. Tounderstand
layer MoS is found to be thisdifference,weexaminethecontributionfromDOSof
2
5
the valence band which is not considered in K·P model. -1.0 V to 1.0 V according to our ab initio results. We
Since the photoinducedcurrentoriginatesfromthe tran- see that the modified coupling polarization is no longer
sition between different valence bands to the same con- anoddfunctionofthegatevoltage,andthebehaviorsof
duction bandwe will neglectthe influence of DOS ofthe ηc(V ) for V = [−1,0.3] V are similar to the results in
g g
conductionband. DOS nearthe topof valence bandwill fi±gure 3(b). In another word, by analyzing the polariza-
be affected by the external electric field. Our ab initio tionofcoupling,onecangettheinformationofthevalley
results show that DOS of valence band are mainly con- polarization. For the monolayer MoS , one can directly
2
tributed by Mo atoms of bilayer MoS . From analytic using the K·P model, but for the bilayer MoS , one has
2 2
calculation, we find that |P (K,s )|2 (|P (K,s )|2) is toconsidertheinfluenceoftheDOSoftheenergybands.
+ z z
related mainly to DOS from lower (upper−) layer of bi-
In summary, we have investigated the photoinduced
layer MoS and |P (K ,s )|2 (|P (K ,s )|2) is related
2 + ′ z ′ z currentoflayeredMoS asa function ofexternalelectric
mainlytoDOSfromupper(lower)−layerofbilayerMoS . 2
2 field. The results show that the valley polarization of
In figure 5(b), we plot the DOS of upper layer Mo atom
photoinducedcurrentof monolayerMoS is independent
2
(red dotted line) and lower layer Mo atom (blue dotted
of external electric field perpendicular to the surface of
line) versus gate voltage obtained by ab initio method.
the layeredMoS whichcanbe inducedbythe gatevolt-
2
From this figure, we see that the influence of external
age, but the valley polarization of photoinduced current
electric field onDOSof Mo atomofupper layeris differ-
of bilayer MoS is very sensitive to the external electric
2
ent from that of lower layer. In another word, a better
field that breaks the inversion symmetry. Moreover, the
definition of valley coupling polarizations should include
valleypolarizationcanbetunedbychangingthepolarity
the effect of DOS as follows,
of circular polarized light. The modulation of valley po-
larizationoflayeredMoS transistorbygatevoltagesand
D cos2α −D sin2α +D cos2α −D sin2α 2
ηc =± l 1 u 1 l 2 u 2. polaritiesofcircularpolarizedlightprovideextraknotin
± Dlcos2α1+Dusin2α1+Dlcos2α2+Dusin2α2 future application of valleytronic devices.
(13)
whereD andD areDOSoflowerandupperMoatoms,
l u
respectively. In panel (c) of figure 5, we plot the modi-
fied coupling polarization as a function of ∆U using Eq. This work was supported by National Natural Science
(13) with DOS taken from the panel (b) of figure 5. In Foundation of China (No.11374246, No.11574217, and
order to compare with figure 3, we changed the abscissa No.11504240 ) and Shenzhen Natural Science Founda-
of panel (c) from ∆U from -0.04 V to 0.04 V to V from tion (JCYJ20150324140036832).
g
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