Table Of ContentEnabling valley selective exciton scattering in monolayer WSe through upconversion
2
M. Manca1, M. M. Glazov2, C. Robert1, F. Cadiz1, T. Taniguchi3, K. Watanabe3,
∗
E. Courtade1, T. Amand1, P. Renucci1, X. Marie1, G. Wang1, and B. Urbaszek1
† ‡
1 Universit´e de Toulouse, INSA-CNRS-UPS, LPCNO,
135 Av. Rangueil, 31077 Toulouse, France
2 Ioffe Institute, 194021 St.Petersburg, Russia
3 National Institute for Materials Science,
Tsukuba, Ibaraki 305-0044, Japan
Excitons,Coulombboundelectron-holepairs,arecompositebosonsandtheirinteractionsintra-
7 ditional semiconductors lead to condensation and light amplification. The much stronger Coulomb
1 interactionintransitionmetaldichalcogenidessuchasWSe monolayerscombinedwiththepresence
2
0 of the valley degree of freedom is expected to provide new opportunities for controlling excitonic
2 effects. But so far the bosonic character of exciton scattering processes remains largely unexplored
in these two-dimensional (2D)materials. Here we show that scattering between B-excitons and
n
a A-excitons preferably happens within the same valley in momentum space. This leads to power
J dependent, negative polarization of the hot B-exciton emission. We use a selective upconversion
technique for efficient generation of B-excitons in the presence of resonantly excited A-excitons at
0
lower energy, we also observe the excited A-excitons state 2s. Detuning of the continuous wave,
2
lowpowerlaserexcitationoutsidetheA-excitonresonance(withafullwidthathalfmaximumof4
] meV) results in vanishing upconversion signal.
l
l
a
h In semiconductors the optical properties are governed ity polariton physics [42–52].
-
by excitons, bound electron-hole pairs [1–6] with certain We introduce an original optical excitation scheme to
s
e analogies to the hydrogen atom. The exciton energy study exciton scattering in the model 2D TMDC mono-
m
states and polarization selection rules need to be under- layer material WSe . We provide a unique situation for
2
. stoodfordesigningoptoelectronicapplicationswhichtar- efficient generation of B-excitons in the presence of reso-
t
a get efficient emission and strong light-matter interaction nantlyexcitedA-excitonsatlowerenergy. Weresonantly
m [7]. Excitonsalsoprovidearichplatformforfundamental excite the A-exciton with a low power laser using an ex-
- physics experiments [8–12]. A real breakthrough for ex- tremely high quality sample with only 4 meV FWHM
d
citonphysicsinthesolidstatewastoshowthatexcitons transition linewidth. Surprisingly, we observe emission
n
behave like composite bosons [13–15]. The key effect is from the B-exciton, 430 meV above the A-exciton state
o
stimulated scattering: Bosons preferentially scatter to a and also of the excited A-exciton (2s) 130 meV above
c
[ quantum state that is already occupied. These pioneer- the fundamental, 1s, state, which we refer to for brevity
ing works enabled studies into optical amplifiers based as ’upconversion’ PL. For circularly polarized excita-
1
on excitons and also new fundamental research on exci- tion we show that the upconverted B-exciton emission
v
ton Bose-Einstein condensation, which are still ongoing isstronglycross-circularlypolarized,thepolarizationde-
0
0 [16–20]. gree increases with laser excitation power. This can be
8 Our target in this work is to look for fingerprints of interpretedasafirstfingerprintofbosonscatteringof2D
5 bosonic interactions in 2D materials. Excitons in tran- excitons[13–15]thatfavoursrelaxationfromtheB-toA-
0 sition metal dichalcogenide (TMDC) monolayers (MLs) excitons within the same valley in momentum space due
.
1 provide exciting new opportunities for applications and tothechiralopticalselectionrules. Possiblemechanisms
0 new frontiers in exciton physics for several reasons: (i) of the upconversion in ML WSe are discussed [53] and
2
7 with binding energies of several hundred meV [21–27], compared to upconversion reported for more traditional
1
excitons dominate optical properties even at room tem- nanostructures such as InP/InAs heterojunctions, CdTe
:
v perature, (ii) the strong exciton oscillator strength leads quantum wells and InAs quantum dots [54–58].
i to absorption of up to 20 % per monolayer [28, 29], and
X
(iii) the interband selection rules are valley selective. In
RESULTS.
r
combination with strong spin-orbit (SO) splittings this
a Upconversion emission 430 meV above excitation
allowsstudyingspin-valleyphysics[30–35]. Theseunique
laser. We study WSe MLs encapsulated in hexagonal
excitonic properties make ML TMDCs ideal systems for 2
boron nitride (h-BN) [59]. The aim is to eliminate detri-
investigating exciton interactions [36–41] and microcav-
mental surface effects [41] and to provide a symmetric
(top/bottom) dielectric environment to study excitons.
The high optical quality of the sample is demonstrated
in Fig. 1c: Here we show reflectivity spectra using a
∗Electronicaddress: [email protected]ffe.ru white light source for illumination. We detect the A
†Electronicaddress: g [email protected]
exciton peak at 1.723 eV, with a linewidth of typically
‡Electronicaddress: [email protected]
4 meV, this main exciton transition is labelled 1s in
2
(a) tiveR A:1s Reflectivity c f SiO2
Exciton vaR/ h-BN
riD
e
t D of A:2s B:1s h-BN
y 1s
x T d 1ML WSe2
A:1s PL
(b)
))
E Free carrier b. u.b. u. A:2s Laser g
states rr
... (a(a X 30 hBN
n=2 y y
EEBB nsitnsit T AA::22ss UUppccoonnvveerrssiioonn PPLL e 11LL WWSSee22
n=1 ee
tt hBN
nn
II
Optical CW Laser SiO
((cid:1)W) 2
Gap
X 60 B:1s Si
|0 > 1.7 1.8 1.9 2.0 2.1 2.2
Energy (eV)
FIG. 1: Exciton resonances in linear spectroscopy and upconversion at T=4 K. The sample consists of a WSe
2
monolayer encapsulated in hBN [59]. (a) Strongly bound electron-hole pairs, excitons, dominate optical properties of TMDC
monolayerssuchasWSe . InWSe thereexist2differentexcitonseries. TheB-excitonisabout400meVabovetheA-exciton
2 2
due to spin-obit splitting of the valence band. (b) Excitons have a binding energy E , defined as the difference between the
B
free particle bandgap and the optical bandgap observed in photoluminescence (PL) emission. E is of the order of 500 meV,
B
the first excited state n=2 is about 130 meV above the n=1 state, marked as A:2s and A:1s, respectively, throughout this
manuscript. (c)WehaveperformedreflectivitywithawhitelightsourcetoidentifytheA-andB-excitonatT=4K.Inaddition
we observe an excited states of the A-exciton labelled A:2s. (d) In photoluminescence we observe neutral A-exciton and trion
emission (T), in addition we see hot luminescence of the A:2s state. (e) We also demonstrate upconversion PL: the laser is
tunedtotheA:1s-excitonresonanceandstrongemissionfromB:1sandA:2satmuchhigherenergyisrecorded,inadditionto
thetrionemission(T)atlowerenergy. (f)opticalmicroscopeimageofthestudiedvanderWaalsheterostructure. (g)Scheme
of the side view of the sample.
analogy to the hydrogenic model. About 133 meV as compared to the neutral exciton [63, 64]. Hot PL of
above the A:1s we detect an excited exciton state, as the A:2s is also observed for other laser energies such as
demonstrated before for samples exfoliated onto SiO 1.96 eV (HeNe Laser).
2
[24, 25, 60, 61]. The linewidth of this transition, which The optical spectra shown in Fig. 1e introduce our
wetentativelyascribetothe2sAexciton,isoftheorder upconversion scheme: excitation of the A:1s exciton
of 5 meV. It is accompanied by a smaller peak about (E =1.723 eV) results in strong PL emission at higher
L
25 meV at higher energy which could be related to the energy of the A:2s (E +133 meV) and B:1s exciton
L
A:3s exciton. At 430 meV above the A:1s we detect the (E +430 meV), as well as trion emission (labelled T)
L
B-excitontransition,wheretheA-Bseparationismainly at lower energy E 31 meV. This upconversion is
L
−
given by the valence band SO splitting [62]. achieved using a narrow linewidth, continuous wave
In addition to white light reflectivity, we have also laser and moderate excitation powers in the µW/µm2
performed PL experiments shown in Fig. 1d. Using range, see Methods. Interestingly we also observe
an excitation laser energy resonant with the B-exciton in WSe MLs directly exfoliated onto SiO (no hBN
2 2
transition, we observe in addition to the A:1s exciton in the structure) this upconversion emission for A:2s
emission (4 meV FWHM) and the trion (T) also the and B:1s, see supplement. These observations are
hot A:2s emission (5 meV FWHM), at very similar very surprising and further experiments that aim to
energies as the reflectivity results, indicating negligible clarifytheoriginofthisupconversionareshowninFig.2.
Stokes shifts. It is a signature of the high quality of
our sample, since absence of the Stokes shifts indicates
Investigating the origin of the upconversion
only very weak localization of excitons, if any. The trion
signal. The observed upconversion is extremely energy
emission is detected in PL but not clearly in reflectivity,
dependent: only strictly resonant excitation of the A:1s
which indicates a lower resident electron concentration
excitonresultsinmeasurableupconversionluminescence.
3
1.7 1.8 1.9
a PLE d
upconversion 4K Upconversion PL
1.73 B:1s emission 1.73
V) V)
ergy (e E1x.7c2t.3=eV 4 meV ergy (e EL=1.7c2w3 eLVaser
n n
on E1.72 1.72on E 50K
ati B:1s ati
cit cit
x x
E E E=1.721 eV
L
1.71 A:2s 1.71 u.)u.)
1.8 2.0 2.2 0 80000 rb. rb. 100K
aa
Emission Energy (eV) Intensity (arb. u.) y (y (
b c nsitnsit
100 UU pp ccoonnvveerrssiioonn AB::12ss Continuum sion Intesion Inte EL=1.714 eV
mismis 200K
u.) A : 1 s EE
b.
ensity (ar10 Slope = 1 ✗ ✔ B:1s EL=1.687 eV
nt A:1s 293K
I ✗
r
e L
1 s P
La t E=1.649 eV
W o L
h
C
1 10 100 | 0 > 1.7 1.8 1.9
Excitation Power ((cid:1)W)
Energy (eV)
FIG. 2: Investigating the origin of the upconversion process. Sample temperature T =4 K. (a) Left panel: contour
plot of the upconversion PL intensity for A:2s and B:1s as a function of excitation energy, with a clear resonance at 1.723 eV,
theA:1sexcitontransitionenergy. Rightpanel: TheresonanceinupconversionPLEhasaFWHMofonly4meV.(b)Weshow
power dependence of the upconversion PL intensity at resonance and compare with power dependence of the neutral exciton
excited at the A:2s state in standard PL. Slopes in the range of 10...100 µW are for A:2s=1.1, B:1s=1.25 and A:1s=0.56 (c)
Scenario for upconversion PL based on 2-photon absorption aided by a real intermediate state is presented. (d) Evolution of
upconversion PL of A:2s for T = 4 K up to room temperature, the excitation laser energy is indicated following the shift of
the A:1s exciton resonance with temperature.
The FWHM of the observed resonance in upconversion excited by the laser combine to form a single excited
PLexcitation(PLE)isabout4meV,asshowninFig.2a, state of the electron-hole pair, with the energy being
see red data points. Resonant excitation 31 meV below the sum of exciton energies. As a plausible scenario we
the A:1s state at the trion energy for example [53], does may suggest an Auger-like process, also referred to as
not result in emission at the A:2s and B:1s energies in exciton annihilation [36–39]. In this case the scattering
our experiment. Emission at higher energy than the of two existing excitons results in the transition of one
laser can have several origins [54–58, 65], here important electron forming an exciton to the valence band (i.e.,
information comes from the B-exciton emission: at 430 nonradiative recombination [67]) while the remaining
meVabovethelaserenergymechanismspurelybasedon electron absorbs the released energy and is promoted
phononemission(i.e. lasercooling[66])areveryunlikely to the excited energy band denoted as a continuum f
| i
at the sample temperature T = 4 K. A more probable in Fig. 2c. Subsequently, the excited electron-hole pairs
scenario is 2 photon absorption, made efficient by the looseenergyvia,e.g.,phononemissionandrelaxtowards
A:1s as a real intermediate state. This idea is supported the radiating states, particularly, B:1s and A:2s. As a
by (i) the narrow resonance around the A:1s exciton result, the upconversion intensity scales as N2 , where
A:1s
(Fig. 2a) and (ii) by analysis of the power dependence N istheexcitonoccupancycreatedbythelaser. The
A:1s
of the emission: the upconversion PL evolves with a occupancy N is directly proportional to the intensity
A:1s
slope roughly twice that of the exciton A:1s emission, of the exciton emission from A:1s state, in agreement
see Fig. 2c. This indicates that two excitons resonantly with experiment, see also the detailed discussion in the
4
B:1supconversion PL
a 5(cid:1)W u.) d 50(cid:1)W
b.
PC= -2% ar X/X
sity ( X/Y
n
e
nt
I0
2.05 2.10 2.15 2.20 2.25
b 10(cid:1)W Energy (eV)
u.)u.)
arb. arb. PC= -7% σσ++//σσ-+ e Continuum
y (y (
sitsit
nn
ee
ntnt
I I
c 50(cid:1)W B:1s
stimulated
P = -14% Boson
C A:1s
scattering
r
σ+ se σ-
a
L PL
W
2.05 2.10 2.15 2.20 2.25 C
Energy (eV) | 0 >
FIG.3: CreatingB-andA-excitons: firstsignaturesofbosonscatteringT=4K,E =1.723eV,σ+laserpolarization.
L
(a)B:1supconversionPLdetectedinσ+(black–co-polarized)andσ−(red–cross-polarized)polarizationforalaserpowerof5
µW.(b)Sameas(a),butfor10µW.(c)Sameas(a)butfor50µW.Thevalueofthecircularpolarizationdegreeoftheemission
Pc = IIσσ++−+IIσσ−− isindicatedonthepanel. Asweincreasethepower,theemissionbecomesstronglycross-polarizedwithrespect
to the initial excitation, we generate a negative polarization P < 0. (d) Laser excitation linearly (X) polarized, detection of
c
upconverted PL at B:1s energy in linear X and Y basis. (e) Scheme to explain negative, power depedent polarization of hot
B:1s PL emission observed in panels (a)-(c) based on boson scattering.
supplement. In addition we observe that upconversion well as Auger-type processes are not governed by strict
PL in our sample is detectable for the A:2s state even polarization selection rules. In this context we have
at room temperature, see evolution as a function of verified that linearly polarized excitation and circularly
temperature in Fig. 2d. polarized excitation yield exactly the same intensity of
the upconversion signal [68].
How can we explain the strong, negative polarization
Possibility of boson scattering from B- to
of the B:1s emission? We propose a scenario based
A-exciton levels. In our experiment we resonantly
on stimulated boson scattering [13–15], as sketched in
pump the A-exciton transition. As addressed above,
Fig. 3e. As a first step, we assume excitation creates
presumably an additional photon is absorbed to create a an equal population of σ+ and σ excitons in the
−
second exciton and, ultimately, to generate an electron-
continuum f , as chiral selection rules are relaxed.
hole pair in a high energy continuum state. From there | i
Subsequently the electron-hole pairs relax towards
the electron-hole pairs relax towards the B-exciton, the B:1s state with the same rates for σ+ and σ .
−
where we observe hot luminescence 430 meV above
However, therelaxationfromtheB-excitonstowardsthe
the A-exciton. Very surprisingly the B:1s emissions
ground, A:1s states is polarization-dependent as bosons
is strongly σ polarized following circularly polarized
− preferentially scatter to a quantum state that is already
σ+ excitation i.e. counter-polarized with respect to
occupied : The pump laser creates a majority of co-
the laser, see Fig. 3a-c. A strong indication for the
polarized A-excitons and since excitons are bosons, the
importance of scattering processes comes from power scattering probability of σ+/σ polarized B:1s excitons
−
dependent measurements: for a laser excitation power
towards A:1s excitons grows as (1+Nσ± ) [15], where
of 5 µW we measure 3 2% PL polarization, for A:1s
a stronger excitation p−owe±r of 50 µW the negative NAσ:±1s are the occupancies of correspondingly polarized
A:1s-excitons. As a result, co-polarized B-exciton states
polarization is about 14 2%, see panels a-c in Fig. 3.
− ± get depleted faster than counter-polarized B-excitons.
Observing any polarization at all for these upconversion
This imbalance gives rise to hot B-exciton PL emission
PL signals is extremely surprising, as it is expected
counter-polarized with respect to the excitation laser.
that absorption at high energy continuum states as
5
A:2supconversion PL
a 5(cid:1)W u.) d 50(cid:1)W
b.
P = 22% ar X/X
C y ( X/Y
t
si
n
te 0
n
u.)u.) b 10(cid:1)W I 1.82 1.84 1.86 1.88 1.90 1.92
b. b. σ+/σ+ Energy (eV)
rr
ty (aty (a PC= 29% σ+/σ- eV)eV)1.74 e E + 133 meV
nsinsi y (y ( Laser
ntente ergerg
II c 50(cid:1)(cid:1)W EnEn1.73
n n
oo
P = 28% titi
C citacita1.72
xx
EE A:2s
1.85 1.86 1.87 1.88 1.89
1.82 1.84 1.86 1.88 1.90 1.92
Energy (eV) Emission Energy (eV)
FIG. 4: Photon emission 133 meV above the excitation laser at 4 Kelvin. (a) T = 4 K, E = 1.723 eV σ+ laser
L
polarization. Upconversion PL of A:2s state detected in σ+ (black) and σ− (red) polarization for a laser power of 5 µW.
(b) Same as (a), but for 10 µW. (c) Same as (a) but for 50 µW. (d) Laser excitation linearly (X) polarized, detection of
upconvertedPLatA:2senergyinlinearXandYbasis. (e)ContourplotofA:2supconversionPLasafunctionoflaserenergy,
a Raman feature moving with the laser energy is clearly visible, see supplement for water-fall style plot.
Linearly polarized excitation of A:1s does not induce ing 2 photon absorption, for example, as well as due to
any linearly polarized upconversion emission of B:1s, the exciton to trion conversion through phonon emission
see Fig. 3d. Linear polarization is linked to valley [53]. Just as for the B:1s upconversion, the experiments
coherence [32], which is too fragile to be maintained using linearly polarized lasers do not result in linearly
duringtheupconversionandenergyrelaxationprocesses. polarized emission in Fig.4d.
In summary, we demonstrate upconversion photolu-
minescence in WSe monolayers at energies as high as
2
Polarization of A:2s upconversion emission and 430 meV above the laser energy. The effect occurs for
anti-Stokes Raman at E +133 meV. The upcon- strictlyresonantexcitationofthegroundA-excitonstate
L
version PL of the A:2s transition on the other hand 1s and is most probably related to 2 photon absorp-
is strongly co-polarized with the excitation laser with tion enabled by a real intermediate state. Very surpris-
P 25%,herethedependenceonexcitationlaserpower ingly, the upconverted PL emission of the B-exciton is
c
≈
is rather weak as shown in Fig. 4a-c. We argue that counter-circularly polarized with respect to the excita-
the polarization of the A:2s is similar to the A:1s po- tion laser, which provides a fingerprint of stimulated ex-
larization as the exciton populations of the two states citonscatteringfromB-toA-states,whichefficientlyde-
are coupled. First, the A:2s to A:1s separation is only pletes the co-polarized B-exciton state. We also show
133 meV, compared to the B:1s to A:1s separation of upconversionemissionatanenergycorrespondingtothe
430 meV. Second, we observe anti-Stokes Raman scat- excited state of the A-exciton 2s. Here strong phonon
tering superimposed on the hot PL of the A:2s exciton, effects are visible in the form of anti-Stokes emission
as can be seen in Fig. 4e and in the supplement. Previ- which exactly shifts with the excitation laser energy E
L
ously, we have reported double resonant Stokes Raman as E +133 meV.
L
scattering [60], that showed efficient relaxation from the
A:2s state to the A:1s state as they are separated by a METHODS.
phonon-multiple. Here the equivalent anti-Stokes pro- Samples. The WSe ML flakes are prepared by
2
cessisvisibleintheexperiments. Duetoefficientphonon micro-mechanical cleavage of a bulk crystal (from 2D
exchange between the A:1s and A:2s states the polariza- Semiconductors) and deposited using a dry-stamping
tionsofthegroundandexcitedstateshavethesamesign. technique on hexagonal boron nitride [59] on SiO /Si
2
NotethatwecannotprobetheA:1spolarizationdirectly substrates. Subsequently h-BN was deposited on top of
in resonant excitation conditions (signal is obscured by the WSe . Figure 1d shows an optical microsope image
2
scattered laser light). In these experiments at T = 4 K of the fabricated van der Waals heterostructure.
the phonons can be generated by the relaxation follow- Experimental Set-up. Low temperature PL and re-
6
flectance measurements were performed in a home build synchronously pumped by a mode-locked Ti:Sa laser.
micro-spectroscopy set-up build around a closed-cycle, The typical pulse and spectral width are 1.6 ps and 3
low vibration attoDry cryostat with a temperature con- meV, respectively; the repetition rate is 80 MHz [69].
troller(T =4Kto300K).ForPLatafixedwavelength The white light source for reflectivity is a halogen lamp
of 633 nm a HeNe laser was used, for PL experiments with a stabilized power supply. The emitted and/or
as a function of excitation laser wavelength we used reflected light was dispersed in a spectrometer and
a tunable, continuous wave Ti-Sa Laser SolsTis from detected by a Si-CCD camera. The excitation/detection
MSQUAREDallowingcontinuoustuningintherangeof spot diameter is 1µm, i.e. smaller than the typical
≈
700-1000 nm. For wavelength below 700 nm the sample ML diameter.
is excited by picosecond pulses generated by a tunable
frequency-doubled optical parametric oscillator (OPO)
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8
the manuscript with input from all the authors.
Author Contributions.— M.M., G.W., F.C. and
E.C. performed the measurements. K.W. and T.T. grew
the hBN. C.R. and P.R fabricated and tested the van Additional information Competing financial inter-
der Waals heterostructures. M.M.G, T.A., X.M. and ests: The authors declare no competing financial inter-
B.U interpreted the data, B.U., G.W. and M.M.G wrote ests.
Enabling valley selective exciton scattering in monolayer WSe through upconversion:
2
Supplementary Information
M. Manca1, M. M. Glazov2, C. Robert1, F. Cadiz1, T. Taniguchi3, K. Watanabe3,
∗
E. Courtade1, T. Amand1, P. Renucci1, X. Marie1, G. Wang1, and B. Urbaszek1
† ‡
1 Universit´e de Toulouse, INSA-CNRS-UPS, LPCNO,
135 Av. Rangueil, 31077 Toulouse, France
2 Ioffe Institute, 194021 St.Petersburg, Russia
3 Advanced Materials Laboratory,
National Institute for Materials Science,
Tsukuba, Ibaraki 305-0044, Japan
7
1
0
2 EXPERIMENTS
n In the main text upconversion and its polarization de- 1800
a pendence is studied in detail for ML WSe encapsulated
J 2 1600
inhexagonalboronnitride(hBN)[S1]. ThishBN/1ML u.)u.) Excitation
0 WSe /hBNhasbeenchosenforitsthespectrallysharp b. b. 1400 Energy
2 2 arar
] aBnudtitnhteenrseepoexrtceitdonefftercatnssiatrieonnso,tseoenFlyigo.bSs1erbvoetdtoinmepnacnaepl-. ensity (ensity ( 111020000000 1111....777712229011 eeeeVVVV
-hall mssuioolnantoweldahyesenarmsexdpciliretesic.ntgWlyteheexafAloslo:i1asotberdseesorovnnetaonvteSlriyyOi2ns,tsrsoteanengFduaigpr.dcSoW1nvSteoerp2- Offset PL IntOffset PL Int 680000 1111111.......777777722222232356792 eeeeeeeVVVVVVV
s panel and also in uncovered samples 1ML WSe2 / hBN 400 1.734 eV
e 1.737 eV
1.739 eV
m 200 1.742 eV
1.84 1.86 1.88 1.90 1.92
.
t Energy (eV)
a
m
FIG. S2: Upconversion PL of A:2s state as a function of
-
d excitation laser energy. The laser energy EL is indicated for
n eachspectrum. ThedataisthesameasinFig.4einthemain
o text, just plotted in a different format.
c
[
1 (middle panel).
v InadditiontotheA:2shotPLemissionfromupconver-
0 sion we also observe anti-Stokes Raman scattering. This
0 can be seen in Fig. S2, where in addition to the A:2s a
8
peak 133 meV above the laser energy is clearly visible in
5
each spectrum, shifting as a function of the laser energy
0
E . This is the same data as in Fig. 4e in the main text.
. L
1 In Fig. S3 we plot circularly co- and cross-polarized
0
emissioninblackandred,respectively,oftheA:2supcon-
7
versionPL.ThecircularpolarizationdegreeP isplotted
1 c
in blue. The polarization of the upconverted emission at
:
v FIG. S1: In the main text the upconversion and its polar- the A:2s energy does not originate exclusively from the
i ization dependence is studied in detail for hBN / 1ML WSe
X 2 anti-stokes Raman process, the emission is globally po-
/ hBN (bottom panel) because of the spectrally sharp and
larized, not just at the Raman energy E +133 meV.
r intense exciton transitions. But this effects is not linked to L
a The A:1s resonance is at 1.723 eV, so the top (bottom)
encapsulation, very strong upconversion when exciting the
panel shows excitation 3 meV above (2 meV below) res-
A:1s resonantly is also observed for vacuum / 1ML WSe /
2
onance. The middle panel corresponds to resonant A:1s
SiO (top panel), and vacuum / 1ML WSe / hBN (middle
2 2
panel). excitation.
MODELS
One-photon absorption. In linear absorption one
absorbed photon generates one exciton. Hence, for reso-
nant excitation of the A:1s state the exciton occupancy
∗Electronicaddress: [email protected]ffe.ru
N is directly proportional to the light intensity I. In
†Electronicaddress: g [email protected] A:1s
‡Electronicaddress: [email protected] thelinearregimetheexcitongenerationratecanbecon-
2
600
1.726 eV c.b.'
40
20
c.b.
0 0
u.)u.)
arb. arb. 900 1.723 eV 40%)%)
sity (sity ( 20Pol. (Pol. (
L IntenL Inten 0 0 Circ. Circ. v.b.
PP
1.721 eV
400 40 FIG.S4: Sketchofthetwo-photonexcitationwitharealin-
termediate state. Open circle denotes the empty state in the
valenceband(v.b.),filledcircledenotesoccupiedstateinthe
20
conduction band (c.b.). The arrow denotes the transition to
thefinalstate(intheremoteconductionbandc.b.’) through
0
0 absorption of a second photon. The Coulomb interaction in-
ducesspreadoftheelectron-holepairink-space(notshown)
1.82 1.84 1.86 1.88 1.90
relaxingthemomentumconservationlaw. Thebandgapsand
Energy (eV) dispersion are not shown to scale.
FIG. S3: Circulalry polarized excitation, co-circular detec-
tion(black)andcross-circular(red)detectionofA:2supcon- of the excitons in the highly excited states denoted as
version PL at T=4K signal (left axis). The circular polariza- f in Fig. 2c of the main text (energy equals to 2~ω, i.e.
tion degree is plotted in blue (right axis). The laser energy |twiice the laser energy) is proportional to the square of
EL is indicated for each panel. incident radiation intensity [S3–S5]
G2PA I2. (S2)
veniently presented as [S2] f ∝
I In the studied situation the single photon energy ~ω
G= (1 ) . (S1)
equals to the A:1s-exciton energy. Hence, the intermedi-
A −R ~ω
ate state for the two-photon process can be real. The
Here is theabsorption coefficient of theTMD ML and
two-photon excitation via real state (RS-2PA) can be
A
is the reflection coefficient of the sample, ~ω is the viewed as a two-step process: creation of the A-exciton
R
photon energy. Due to nonlinear effects, e.g., absorption
at the first step and transition of the A-exciton to the
saturation, or nonlinear (Auger) recombination of exci-
excited f state via the second photon absorption. On
tons the exciton occupancy can be sublinear function of | i
the level of free electron-hole pairs the process is illus-
the incident light intensity. The exciton occupancy
trated in Fig. S4. In this process the generation rate of
the excited excitons takes the form
N Gτ ,
A:1s A
∝
whereτA isthelifetimeoftheA-exciton. Thenonlinear- GRfS−2PA ∝NA:1sI. (S3)
ities are either included in the intensity dependence of
the absorption coefficient = (I) or in the exciton oc- This dependence is weaker than I2 due to possible satu-
A A
cupancydependenceofexcitonlifetime, τ =τ (N ). ration of linear absorption. Particularly, if intermediate
A A A:1s
The analysis of the particular origin of the sublinear be- states saturate GRfS−2PA ∝I.
havior of N vs. intensity seen in Fig. 2b of the main Moreover,twophotonscanbeabsorbedindependently
A:1s
text is beyond the scope of the present work. resulting in formation of two A:1s-excitons as schemat-
Two-photonabsorptionandAuger-likeprocess. ically shown in Fig. S5a. The Coulomb interaction be-
The observation of B:1s exciton emission at A:1s excita- tween the charge carriers forming the excitons results in
tion is possible if any only if, in addition to the pho- the redistribution of the excitation in the k- and energy-
togenerated exciton, another quantum: second exciton, spaces. Particularly, the Auger-like process is possible.
photonorphononisinvolved. Otherwisetheenergycon- InthisscenarioduetotheCoulombscatteringoneofthe
servation law is violated. Let us consider in more detail interacting electrons goes to the unoccupied state in the
the processes without phonon involvement. valence band, while another one takes the released en-
Standard two-photon absorption (2PA) involves a vir- ergy and gets promoted to the excited energy band [S6].
tual intermediate state. In this case the generation rate Asaresult,theexcited f stateoftheelectron-holepair
| i
