Photoinduced Bandgap Renormalization and Exciton Binding Energy

Subscriber access provided by READING UNIV

Article

Photoinduced Bandgap Renormalization and Exciton Binding Energy Reduction in WS 2

Paul D. Cunningham, Aubrey T Hanbicki, Kathleen M. McCreary, and Berend T. Jonker ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b06885 • Publication Date (Web): 11 Dec 2017 Downloaded from http://pubs.acs.org on December 14, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Nano is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Photoinduced Bandgap Renormalization and Exciton Binding Energy Reduction in WS2 Paul D. Cunningham*, Aubrey T. Hanbicki, Kathleen M. McCreary, Berend T. Jonker U.S. Naval Research Laboratory, Washington, DC 20375, United States *[email protected]

ACS Paragon Plus Environment

1

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 25

ABSTRACT

Strong Coulomb attraction in monolayer transition metal dichalcogenides gives rise to tightly bound excitons and many body interactions that dominate their optoelectronic properties. However, this Coulomb interaction can be screened through control of the surrounding dielectric environment as well as through applied voltage, which provides a potential means of tuning the bandgap, exciton binding energy, and emission wavelength. Here, we directly show that the bandgap and exciton binding energy can be optically tuned by means of the intensity of the incident light. Using transient absorption spectroscopy, we identify a sub-picosecond decay component in the excited state dynamics of WS2 that emerges for incident photon energies above the A exciton resonance, which originates from a non-equilibrium population of charge carriers that form excitons as they cool. The generation of this charge carrier population exhibits two distinct energy thresholds. The higher threshold is coincident with the onset of continuum states and therefore provides a direct optical means of determining both the bandgap and exciton binding energy. Using this technique, we observe a reduction in the exciton binding energy from 310 ± 30 meV to 220 ± 20 meV as the excitation density is increased from 3 x 1011 photons/cm2 to 1.2 x 1012 photons/cm2. This reduction is due to dynamic dipolar screening of Coulomb interactions by excitons, which is the underlying physical process that initiates bandgap renormalization and leads to the insulator-metal transition in monolayer transition metal dichalcogenides.

TOC GRAPHICS


2

Page 3 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

KEYWORDS:

dynamic screening, Coulomb interaction, exciton formation, many-body,

transition metal dichalcogenide, 2D materials, ultrafast spectroscopy

The binding energy of excitons in low-dimensional materials is an important fundamental property and depends on the Coulomb coupling strength between electrons and holes. However, it has proven difficult to directly determine the exciton binding energy in two-dimensional monolayer transition metal dichalcogenides (TMDs), which requires measuring both the exciton resonance and the electronic bandgap. Previously it has been inferred from reflectance contrast,1, 2

absorbance,3 ellipsometry,4 fluorescence excitation profiles,5 and two-photon excitation

spectroscopy.6 The binding energy can also been estimated from optical scanning tunneling spectroscopy7 as well as from diamagnetic shifts if the exciton reduced mass is known.8,

9

Recently, there has been much interest in tuning the Coulomb coupling strength through screening effects caused by changes to the surrounding media10, 11 or applied external fields12, 13 in order to control the electronic band gap, exciton binding energy, or emission wavelength. In the latter effect, an applied voltage injects equilibrium charge carriers that efficiently screen


3

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 25

Coulomb interactions. Unlike these static modifications to the electronic structure, nonequilibrium changes in Coulombic screening and subsequent bandgap renormalization should occur after the absorption of light, though only changes in the exciton resonance have been directly observed.14,

15

It has recently been theoretically predicted that dipolar screening by

photoexcited excitons plays a crucial role in band gap renormalization and causes selfamplifying exciton ionization,16 ultimately leading to a Mott insulator-metal transition. The steady state techniques previously used to estimate the exciton binding energy are not capable of resolving these non-equilibrium changes. Instead, direct measurements of photoinduced changes in the exciton binding energy are needed to understand the role of dipolar screening in bandgap renormalization. Such measurements may help elucidate the exciton dissociation mechanisms that are responsible for efficiently producing photocurrent in photodetectors based on TMDs. An understanding of how Coulombic screening can be used to influence electronic properties is also crucial to the design of van der Waals heterostructures,17 where screened Coulomb interactions will lead to optoelectronic properties that differ from those in the constituent individual twodimensional layers. Due to quantum confinement and strong Coulomb coupling the absorption spectra of TMDs are dominated by excitonic features, typically labeled A, B, C, and so on with increasing energy. Upon optical excitation, state filling of the A-exciton leads to a reduction in the ground state absorption. This process is referred to as the A-exciton bleach or ground state bleach (GSB).18 We recently reported that a fast decay component appears in the GSB when WS2 is photoexcited at energies significantly above the A exciton resonance.19 This phenomenon was previously observed in MoSe2 and WSe2, where it was conjectured that exciton formation from initially photogenerated unbound charged species was the cause of the decay.20 Here we report two


4

Page 5 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

photoexcitation energy thresholds for this sub-picosecond decay and present detailed measurements showing that the higher of the two thresholds arises from exciton formation following photoexcitation of the continuum states in CVD-grown large-area WS2. As such, observation of this threshold represents a direct optical method of determining the bandgap and exciton binding energy in TMDs. Using this technique to monitor the exciton binding energy, we demonstrate that the exciton binding energy can be tuned from 320 meV to 220 meV by varying the absorbed fluence from 3 x 1011 photons/cm2 to 1.2 x 1012 photons/cm2. This directly confirms that bandgap renormalization occurs in monolayer WS2 upon photoexcitation and demonstrates that the exciton binding energy can be optically tuned via the intensity of incident light.

RESULTS AND DISCUSSION We examined the GSB dynamics in CVD-grown WS2 monolayers at room temperature as a function of excitation photon energy. In this measurement, we recorded the differential transmission (∆T/T0) of a white light probe beam in the region of the GSB maximum located at 616 nm (2.013 eV) as a function of time after photo-excitation at selected energies by a pulsed laser, Figure 1, for a constant absorbed fluence of 9 ± 1 x 1011 photons/cm2. This is a moderate excitation density that is below the estimated Mott density of approximately 1013 cm-2,16, 21 at which WS2 transitions from an insulator to a metal. For near-resonant excitation at 612 nm (2.026 eV) of the A exciton (2.013 eV), photogenerated excitons decay primarily through nonradiative exciton-exciton annihilation (EEA), also referred to as Auger recombination, on a 10s of picosecond timescale.19,

22

As the excitation photon energy is increased, a sub-picosecond

decay emerges. This decay feature becomes more prominent as the photon energy is increased further, as can be seen in Figure 1.


5

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 25

Figure 1. Emergence of sub-picosecond excited state decay component in WS2. Photoexcitation wavelength dependent dynamics of the A-exciton bleach located at 616 nm (2.013 eV) for 9 ± 1 x 1011 cm-2 photoexcitation from 612 nm (2.026 eV) to 515 nm (2.408 eV). The black arrows indicate the values used to create the amplitude ratio of the peak A-exciton bleach (∆Tmax) to the value measured 3ps later (∆T(+3ps)). Inset: The absorbance of WS2, with the A, B, and C excitons labeled. The colored arrows indicate the various photoexcitation wavelengths.


6

Page 7 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Figure 2. Comparison of WS2 response to low and high energy photons. (a - b) Time evolution of the differential transmission and (c - d) the absorption coefficient of monolayer WS2 after photoexcitation at (a & c) 590 nm, ∆E = 89 meV, and (b & d) 515 nm, ∆E = 395 meV as measured by transient absorption spectroscopy. The center wavelength of the A exciton absorption in (c - d) is indicated with a dashed white line. The dashed black line is the approximate time at which the pump and probe are temporally overlapped.

To elucidate the operative photophysical processes that give rise to the observed sub-picosecond dynamics, we recorded the time evolution of the photo-induced changes to the excited state spectrum using transient absorption spectroscopy (TA) for excitation energies above and below


7

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 25

the photon energy required to excite the sub-picosecond decay feature in Figure 1. The two excitation photon energies compared in Figure 2 are 2.102 eV (590 nm) and 2.408 eV (515 nm). In these two cases the excitation photons have excess energies above the A-exciton level, defined as ∆E = hν –EA, of 89 meV and 395 meV respectively. In both cases we observe spectra that can be described by changes in absorption amplitude, linewidth, and center wavelength. Similar analysis has previously been applied to identify charge trapping in MoS2.23 After the first picosecond, the excited state dynamics for both photon energies are dominated by 1) the rapid decay of the A-exciton GSB amplitude near 616 nm, 2) a reduction in the initial photo-induced spectral broadening, and 3) a red shift that grows in over picoseconds and decays over tens of picoseconds. The rapid change in GSB amplitude has previously been assigned to EEA, which dominates for fluences above 1010 cm-2.19, 22 While changes in amplitude can be readily observed from TA data traditionally expressed as differential transmission, ∆T/T0, (Figure 2 a, b) spectral shifts are more unambiguously identified when we instead calculate the time-dependent absorption spectrum from the raw data (Figure 2 c, d). The details of this calculation are in the Supporting Information. The picosecond-scale red-shift dynamics we observe from t ~ 1 – 10 ps have recently been assigned to lattice heating caused by phonon emission from the hot excitons that result from EEA.18 At early delays, near t ~ 1ps, we see a small initial blue shift of the Aexciton resonance, which may be due to Pauli blocking of the exciton band edge via the Bernstein-Moss effect24 or due to the effects of dynamic screening of Coulomb interactions,25 that precedes the aforementioned red shift present at later delays.


8

Page 9 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Figure 3. Analysis of WS2 response to low and high energy photons. Time evolution of the Lorentzian fit parameters to the A exciton absorption spectrum of monolayer WS2 after photoexcitation at (a-c) 590 nm, ∆E = 89 meV, and (d-f) 515 nm, ∆E = 395 meV, as measured by transient absorption spectroscopy. (a) and (d) compare the normalized change in amplitude. (b) and (e) compare the normalized change in linewidth, where time scales dominated by charges, exciton formation, exciton-exciton annihilation are indicated. (c) and (f) compare the normalized change in absorption resonance energy, where the blue- and red-shifted regions are indicated. The vertical dashed lined is the approximate time at which the pump and probe pulses are temporally overlapped.

Quantifying the observed normalized shifts in the A exciton resonance energy, ∆hν/hν0, normalized changes in absorption linewidth, ∆w/w0, and normalized changes in absorption amplitude, ∆/ , can be accomplished by fitting the absorption spectra with a Lorentzian profile at each time delay and following the temporal evolution of the fit coefficients, Figure 3.


9

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 25

The Supporting Information provides details concerning the fitting procedures. For both photon energies, the initial A-exciton resonance blue-shift (Figures 3 c, f) peaks near t ~ 1 ps and likely originates from Pauli blocking of the exciton band edge and changes in the A-exciton transition energy due to dynamic screening of Coulomb interactions. Screening of Coulomb repulsion leads to a decrease in the electronic bandgap, which is often referred to as bandgap renormalization.26 Simultaneously, screening of Coulomb attraction decreases the exciton binding energy such that these two changes only partially cancel,14, 25 and can give rise to either a comparatively small red-shift or blue-shift of the A-exciton resonance depending on the exciton density.15 A similarly blue-shifted A exciton absorption peak has also been previously observed in optically excited monolayer MoS2.27 The blue-shift we observe evolves into a red-shift due to lattice heating that results from EEA.18 The change in amplitude (Figures 3 a, e) that occurs after t ~1 ps has been associated with EEA limited decay kinetics.19,

22

The simultaneous decay in

linewidth broadening (Figures 3 b, e) is also dominated by EEA dynamics. Because excitonexciton scattering may give rise to the linewidth broadening,27-29 the decrease in exciton population caused by EEA reduces the absorption linewidth. The main differences between the TA spectra measured for high and low excitation energies are present at early times. For the lower photon energy, ∆E = 89 meV, the A-exciton resonance blueshift observed at early delays shows an initial peak during the pump-probe overlap near t ~ 300 fs, Figure 3c, which is missing for higher photon energies. This instrument limited shift may originate from the optical Stark effect,30 which should be enhanced for near resonant excitation. For the higher photon energy, ∆E = 395 meV, we observe an additional peak in the spectral broadening (∆w/w0) and GSB (∆/ ) of the absorption amplitude near t ~ 500 fs, Figures 3e & d respectively. The presence of charge carriers can explain both of these additional dynamics.


10

Page 11 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

In quantum-confined semiconductors where the optoelectronic properties are dominated by excitons, initially photoexcited nonequilibrium charge carriers form excitons as they cool.31 Very recently, this process was directly observed in monolayer WSe2.32 Charge carriers can be twice as effective at bleaching the ground state as excitons,20 so that the additional peak in ∆/ could be caused by charge carriers that are not generated at lower photon energies. Charge carrier scattering can also explain the additional absorption linewidth broadening via either carrier-phonon or carrier-carrier scattering mechanisms.18, 23, 33 Exciton formation that occurs as these initially hot carriers cool could therefore cause the observed ultrafast decay in ∆/ and commensurate decrease in linewidth broadening between t ~ 0.5 – 1ps. The sub-picosecond time-scale of these ultrafast dynamics is consistent with recent infrared measurements of exciton formation dynamics in WSe2,32 as well as theoretical predictions34 and experimental measurements of carrier cooling times via carrier-phonon scattering33 in TMDs. Though a red shift of the absorption spectrum may be intuitively expected for charge carrier generation, such shifts have only been observed in WS2 near the insulator metal transition,15,

21

and are not

predicted for the comparatively low excitation densities used here.35


11

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 25

Figure 4. Optical tuning of the exciton binding energy in WS2. Dependence of the amplitude ratio ∆Tmax/∆T(+3ps) on ∆E, the difference between the photon energy (hν) and the A exciton resonance (EA) located at 616 nm (2.013 eV) for photon fluences of (a) 3 ± 1 x 1011 cm-2 and (b) 1.2 ± 0.1 x 1012 cm-2. Dash lines indicate two thresholds labeled 2s and Eb. The solid line is a phenomenological fit described in the Supporting Information used to quantify Eb. The illustrations in (c) and (d) show the Rydberg progression and the electronic band gap, Egap, corresponding to the two cases in (a) and (b) respectively.

To gain further insight into the nature of this hot-electron regime, we analyzed the photon energy dependence of the sub-picosecond GSB decay feature by taking the ratio of the peak ∆T/T0 amplitude to a background value measured 3 ps later (∆T/T0 (+3ps)), after this fast feature has decayed, indicated by arrows in Figure 1. These measurements were carried out at constant


12

Page 13 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

absorbed fluences of 3 ± 1 x 1011 and 1.2 ± 0.1 x 1012 photons/cm2. Fluences were kept below 2 x 1012 photons/cm2 so that rapid EEA19 would not obscure the exciton formation dynamics. This was accomplished by maintaining a constant GSB amplitude at 10ps, which is after exciton formation is completed and therefore ∆T/T0 (10 ps) will be proportional to the exciton population. A summary of the results is plotted in Figure 4, where the ratio of peak amplitude to background is plotted as a function of excess energy, i.e. the energy difference between the excitation and the A exciton, ∆E = hν –EA. From these data it is clear that two thresholds are present. For ∆E >143 meV (575 nm) we see a fast decay feature emerge independent of excitation density. For a low excitation density of 3 x 1011 photons/cm2, Figure 4a, we see additional peaks for ∆E between 200 – 280 meV, (560 – 540 nm), and then a second threshold is present for ∆E ~ 310 ± 30 meV. Above this second threshold we see that the relative fraction of the GSB that decays on a sub-picosecond timescale increases with increasing photon energy. For a higher excitation density of 1.2 x 1012 photons/cm2, Figure 4b, the additional peaks are absent and the second threshold appears at a lower photon energy of ∆E ~ 220 ± 20 meV. Two thresholds were previously observed for MoSe2 and WSe2 by Ceballos et al.,20 though only the lower of the two was discussed in terms of the electronic band gap. Because the higher energy threshold we observe is below the WS2 B exciton energy, we cannot assign it to the binding energy of the B exciton. We instead find that these features correspond more closely to literature reports of the Rydberg states and the onset of continuum states in WS2,1 Figure 4 c-d, which are expected to depend on the excitation density.12, 15, 16, 36


13

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 25

Figure 5. Confirmation of the Rydberg Series and exciton binding energy in WS2. a) Absorption spectrum and b) low-intensity steady-state photoluminescence excitation spectrum of A exciton emission from monolayer WS2 collected at 616 nm (2.013 eV) at room temperature. (c) The second derivative of the photoluminescence excitation spectrum. Dashed lines indicate the Rydberg progression as well as the A, B, C, and D exciton features. The peak near 455 nm is a Raman feature from the fused silica substrate. (d) Illustration of the Rydberg progression of electron states in a Coulomb potential with increasing principal quantum numbers, n, and their convergence into ionized states. (e) Comparison between the Rydberg energies measured here and those reported by Chernikov, et al.1 The red dashed line represents the estimation of the exciton binding energy, Eb, therein. The black dotted line is a guide.


14

Page 15 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

To better understand the origin of the photon energy thresholds, we measured the photoluminescence excitation spectrum (PLE) of monolayer WS2, Figure 5b. Here we record the intensity of the emission collected at a wavelength of 616 nm (2.013 eV) as the excitation wavelength is tuned. In these data we clearly observe contributions of the B, C, and possibly D exciton resonances, which are visible in the absorption spectrum, Figure 5a. We do not observe the strong decrease in the luminescence intensity for excitation above the C exciton previously reported and assigned to suppressed radiative recombination as a result of band nesting,37 or interpreted as the quasiparticle bandgap.38 Additionally, we observe subtle peaks between the A and B exciton energies located at approximately 560 nm (2.214 eV), 551 nm (2.255 eV), and 539 nm (2.301 eV). These peaks are more readily identified by taking the second derivative of the PLE with respect to wavelength, Figure 5c. The peak locations, Figure 5e, are consistent with previous measurements,1, 5 and theoretical predictions39 of the non-hydrogenic Rydberg series of WS2. We therefore assign these peaks to the 3s, 4s, and 5s states of WS2. From this Rydberg series, exciton binding energies between 270 - 360 meV have previously been estimated.1, 5, 10, 12, 39

The two energy thresholds we observe in GSB dynamics in Figure 4 therefore appear to

correspond to the 2s and continuum states, respectively, while the peaks between 560 – 540 nm approximately correspond to higher Rydberg states that appear in the PLE. Based on the measured Rydberg series and the evidence of charge carriers preceding exciton formation for high excitation energies, we assign the second threshold in Figure 4a to the exciton binding energy in WS2. This is consistent with past estimates of the exciton binding energy (~ 320 meV) based on the observed Rydberg series,1, 4 recent estimates based on diamagnetic shifts in WS2 (~312 meV),9 and first principal calculations (~270 meV).39 We speculate that the 143 meV threshold arises from optically accessing the 2s state and that the features between 200 –


15

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 25

280 meV correspond to higher order Rydberg states, Figure 4c. These assignments are also supported by recent calculations of the excited state dielectric function of WS2.16 For higher excitation densities of ~ 1012 cm-2, Figure 4b, we observe that the exciton binding energy decreases to 220 meV and the higher Rydberg states are no longer identifiable. At high excitation density, higher Rydberg states are no longer bound and instead merge with the continuum states, Figure 4d. This is consistent with recent experimental and theoretical reports that the exciton binding energy in TMDs depends on the extent to which the Coulomb interaction between electrons and holes is screened10, 11 and can therefore be reduced by a high density of charges or excitons.16

Figure 6.

Absorbed Fluence dependence of the exciton binding energy in WS2. The

measured dependence of the 1S (filled circles) and 2S states (open circles) of the A exciton in WS2 from 3 x 1011 cm-2 to 1.2 x 1012 cm-2. The theoretical binding energies (grey), calculated from Steinhoff et al.16 by assuming a low fluence binding energy of 310 meV, are included for comparison. The dashed lines through the data are guides to the eye.


16

Page 17 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

To clarify the effect of dynamic screening on the exciton binding energy in WS2, we determined the binding energy for absorbed fluences between 3 x 1011 cm-2 - 1.2 x 1012 cm-2, Figure 6. The associated amplitude ratio ∆Tmax/∆T(+3ps) as a function of ∆E for each fluence can be found in the Supporting Information. We find that binding energies of both the 1S and 2S states of the A exciton reduce with increasing fluence. The binding energy reduction we observe is smaller than recent theoretical predictions that were based on charge carrier screening of Coulomb interactions.15,

25

This is expected because, in our system, neutral excitons are the majority

photogenerated product over this fluence range and are much less efficient at screening Coulomb interactions than charge carriers. The binding energy reduction we observe is in good qualitative agreement, although somewhat larger, than recent predictions based on dipolar exciton screening of Coulomb interactions.16 This discrepancy may arise due to the equilibrium nature of those calculations or due to the presence of inherent defects in our WS2 that may assist in charge separation by trapping one charge carrier and thereby increasing the Coulomb screening. While screening of the Coulomb attraction decreases the exciton binding energy, simultaneous screening of the Coulomb repulsion leads to a decrease in the bandgap that nearly compensates for the changes in binding energy,14,

25

such that the changes in the A exciton energy are

comparatively small.15 Past studies have resolved only these small changes to the A-exciton energy,14,

15

which have been interpreted in terms of dynamic screening. However, direct

evidence of the underlying changes in the electronic bandgap and exciton binding energy has been elusive. Here we are able to directly show that photo-induced dynamic screening of Coulomb interactions gives rise to reductions in the exciton binding energy and electronic bandgap. At very high excitation densities of ~ 1013 cm-2, the binding energy is expected to


17

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 25

become small enough for the continuum states to merge with the A exciton resonance leading to an insulator metal transition.21, 25, 40 Limitations of our measurement technique prevent reaching high enough fluences to observe the sharp decrease in exciton binding energy due to selfamplifying exciton ionization16 that is predicted to occur just below the Mott transition. Specifically, at such high fluences, fast EEA obscures the exciton formation dynamics.19 Timeand angular-resolved photoemission spectroscopy41,

42

may be better suited to resolve the

dynamics near the Mott transition. The measurements shown here directly confirm that bandgap renormalization occurs in monolayer WS2 following photoexcitation and demonstrate that the exciton binding energy can be optically tuned via the intensity of incident light. The observed two-threshold behavior in Figure 4 may be universal to two-dimensional TMDs. In a previous literature report, two similar thresholds were observed in MoSe2 and WSe2: lower energy thresholds at approximately 150 meV and 200 meV, and higher energy thresholds at approximately 600 meV and 550 meV respectively.20 In both cases, the higher energy thresholds approximately correspond to estimates of the exciton binding energy.11,

26

The lower energy

threshold in WSe2 agrees more closely with the 1s-2s transition,3, 43 while theoretical calculations or direct measurements of the 2s state in MoSe2 have not yet been published to the best of our knowledge. Therefore, the observations presented here appear to be general and measurement of this photon-energy dependent sub-picosecond decay may represent a direct optical means of determining the bandgap and exciton binding energy in semiconducting two-dimensional TMDs. It should be noted that the absorbed fluence dependence of the exciton binding energy might vary significantly between different types of monolayer TMDs. A major reason is that the dark spin-orbit-split conduction band is lower in energy than the bright conduction band in WX2 (X=S, Se), but this situation is reversed in MoX2.44 Therefore, though we cannot observe them


18

Page 19 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

without the use of plasmonics45 or magnetic fields,46 the number of populated dark exciton states outnumber the bright states in WS2 and thereby play an important role in dipolar screening of Coulomb interactions.16 Since these dark excitons are more tightly bound and will ionize less easily in WX2, we may expect a larger change in the exciton binding energy with increased fluence in MoX2 as compared to WX2.

CONCLUSIONS In summary, we have examined the photon-energy dependent excited state dynamics in monolayer WS2 measured via ultrafast transient absorption spectroscopy. We observe a subpicosecond decay component that emerges for photon energies significantly higher than the A exciton resonance. This feature exhibits two thresholds, the lower of which we assign to the ground state-to-2s transition and the higher one that corresponds to excitation of the continuum states within the A exciton manifold, i.e. from the higher energy of the two spin-orbit split valence bands. These assignments are confirmed by identifying the Rydberg series within the fluorescence excitation spectrum. Direct excitation of continuum states yields an initially hot non-equilibrium charge carrier population that forms excitons as it cools, leading to a subpicosecond decay of both the ground state bleach and absorption linewidth broadening. Similar features previously reported in the excited state dynamics of MoSe2 and WSe2 suggest that this phenomenon could be common to 2D semiconducting TMDs. As such, this spectroscopic feature represents a direct optical means of determining the exciton binding energy that may prove useful in understanding changes to many-body physics and exciton dissociation mechanisms in emerging van der Waals heterostructures. Using this technique, we show direct evidence that the


19

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 25

measured bandgap and exciton binding energy are reduced by increasing the excitation density due to dynamic screening.

METHODS Monolayer WS2 on SiO2/Si was prepared by chemical vapor deposition in a 2 inch tube furnace. WO3 powder, and sulfur precursors are heated to 825° C under a 100 sccm argon and 10 sccm hydrogen flow. Perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt is used as seed molecules to promote lateral growth. This procedure was recently shown to produce large (>20 µm) grain uniform coverage monolayer WS2 that exhibits enhanced photoluminescence (PL).47 After growth, the WS2 films were transferred onto fused silica substrates for transmission measurements using a wet transfer technique.23 The monolayer nature of the films were confirmed by Raman and PL mapping.19 The PL spectrum is dominated by the A exciton emission and shows no significant trion character. The transient absorption spectroscopy setup has been detailed elsewhere.23 Monolayer WS2 films were photoexcited using tunable pulses from an optical parametric amplifier (Clark NOPA) and probed with a white-light continuum that was analyzed using a scanning monochromator. To eliminate artifacts in the TA spectra due to scatter from the excitation beam, simultaneous modulation of the pump and probe beams was employed with lock-in detection at the sum of the two modulation frequencies. Measurements of the transmission through the photoexcited and unexcited films allowed for determination of the normalized change in transmission, ∆T/T0. Transmission measurements through the bare substrate allowed for the absorption coefficient to be calculated at each time delay, see Supporting Information for details. Films were kept under


20

Page 21 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

dry air flow at room temperature during all measurements. Linearly polarized pump and probe beams were used. Photoluminescence excitation spectra were measured using a fluorescence spectrophotometer (Agilent Cary Eclipse). PLE spectra were collected at an emission wavelength of 616 nm with a 620 nm (10 nm FWHM) band-pass filter in place to block scattered light from the excitation beam.

SUPPORTING INFORMATION The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.xxxxxxx.

Details concerning the calculation of the photoexcited absorption spectrum from the TA data, Lorentzian fits to the absorption spectrum, phenomenological fit functions used in Figure 4, and the amplitude ratio ∆Tmax/∆T(+3ps) as a function of ∆E for each fluence in Figure 6.

ACKNOWLEDGMENT This work was supported by core programs at the U.S. Naval Research Laboratory (NRL), the NRL Nanoscience Institute, and by the Air Force Office of Scientific Research under contract number AOARD 14IOA018-134141.

AUTHOR CONTRIBUTION


21

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 25

P.D.C. conceived and directed the experiments with help from A.T.H.; K.M.M. synthesized and characterized the monolayer samples; P.D.C. performed TA, PLE, and associated analysis; all authors discussed the results and contributed to the written manuscript.

REFERENCES 1. Chernikov, A.; Berkelbach, T. C.; Hill, H. M.; Rigosi, A.; Li, Y.; Aslan, O. B.; Reichman, D. R.; Hybertsen, M. S.; Heinz, T. F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2. Phys. Rev. Lett. 2014, 113, 076802. 2. Hanbicki, A. T.; Currie, M.; Kioseoglou, G.; Friedman, A. L.; Jonker, B. T. Measurement of High Exciton Binding Energy in the Monolayer Transition-Metal Dichalcogenides WS2 and WSe2. Solid State Commun. 2015, 203, 16-20. 3. He, K.; Kumar, N.; Zhao, L.; Wang, Z.; Mak, K. F.; Zhao, H.; Shan, J. Tightly Bound Excitons in Monolayer WSe2. Phys. Rev. Lett. 2014, 113, 026803. 4. Liu, H.-L.; Shen, C.-C.; Su, S.-H.; Hsu, C.-L.; Li, M.-Y.; Li, L.-J. Optical Properties of Monolayer Transition Metal Dichalcogenides Probed by Spectroscopic Ellipsometry. Appl. Phys. Lett. 2014, 105, 201905. 5. Hill, H. M.; Rigosi, A. F.; Roquelet, C.; Chernikov, A.; Berkelbach, T. C.; Reichman, D. R.; Hybertsen, M. S.; Brus, L. E.; Heinz, T. F. Observation of Excitonic Rydberg States in Monolayer MoS2 and WS2 by Photoluminescence Excitation Spectroscopy. Nano Lett. 2015, 15, 2992-2997. 6. Ye, Z.; Cao, T.; O'Brien, K.; Zhu, H.; Yin, X.; Wang, Y.; Louie, S. G.; Zhang, X. Probing Excitonic Dark States in Single-Layer Tungsten Disulphide. Nature 2014, 513, 214-218. 7. Hill, H. M.; Rigosi, A.; Rim, K. T.; Flynn, G. W.; Heinz, T. F. Band Alignment in MoS2/WS2 Transition Metal Dichalcogenide Heterostructures Probed by Scanning Tunneling Microscopy and Spectroscopy. Nano Lett. 2016, 16, 4831-4837. 8. Stier, A. V.; McCreary, K. M.; Jonker, B. T.; Kono, J.; Crooker, S. A. Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS2 and MoS2 to 65 Tesla. Nat. Commun. 2016, 7, 10643. 9. Plechinger, G.; Nagler, P.; Arora, A.; del Aguila, A. G.; Ballottin, M. V.; Frank, T.; Steinleitner, P.; Gmitra, M.; Fabian, J.; Christianen, P. C. M.; et al. Excitonic Valley Effects in Monolayer WS2 under High Magnetic Fields. Nano Lett. 2016, 16, 7899-7904. 10. Raja, A.; Chaves, A.; Yu, J.; Arefe, G.; Hill, H. M.; Rigosi, A. F.; Berkelbach, T. C.; Nagler, P.; Schüller, C.; Korn, T.; et al. Coulomb Engineering of the Bandgap and Excitons in TwoDimensional Materials. Nat. Commun. 2017, 8, 15251. 11. Stier, A. V.; Wilson, N. P.; Clark, G.; Xu, X.; Crooker, S. A. Probing the Influence of Dielectric Environment on Excitons in Monolayer WSe2: Insight from High Magnetic Fields. Nano Lett. 2016, 16, 7054-7060. 12. Chernikov, A.; van der Zande, A. M.; Hill, H. M.; Rigosi, A. F.; Velauthapillai, A.; Hone, J.; Heinz, T. F. Electrical Tuning of Exciton Binding Energies in Monolayer WS2. Phys. Rev. Lett. 2015, 115, 126802.


22

Page 23 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

13. Yao, K.; Yan, A.; Kahn, S.; Suslu, A.; Liang, Y.; Barnard, E. S.; Tongay, S.; Zettl, A.; Borys, N. J.; Schuck, P. J. Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer MoS2. Phys. Rev. Lett. 2017, 119, 087401. 14. Pogna, E. A. A.; Marsili, M.; Fazio, D. D.; Conte, S. D.; Manzoni, C.; Sangalli, D.; Yoon, D.; Lombardo, A.; Ferrari, A. C.; Marini, A.; et al. Photo-Induced Bandgap Renormalization Governs the Ultrafast Response of Single-Layer MoS2. ACS Nano 2016, 10, 1182-1188. 15. Sie, E. J.; Steinhoff, A.; Gies, C.; Lui, C. H.; Ma, Q.; Rösner, M.; Schönhoff, G.; Jahnke, F.; Wehling, T. O.; Lee, et al. N. Observation of Exciton Redshift−Blueshift Crossover in Monolayer WS2. Nano Lett. 2017, 17, 4210-4216. 16. Steinhoff, A.; Florian, M.; Rösner, M.; Schönhoff, G.; Wehling, T. O.; Jahnke, F. Exciton Fission in Monolayer Transition Metal Dichalcogenide Semiconductors. Nat. Commun. 2017, 8, 1166. 17. Geim, A. K.; Grigorieva, I. V. Van der Waals Heterostructures. Nature 2013, 499, 419-425. 18. Ruppert, C.; Chernikov, A.; Hill, H. M.; Rigosi, A. F.; Heinz, T. F. The Role of Electronic and Phononic Excitation in the Optical Response of Monolayer WS2 After Ultrafast Excitation. Nano Lett. 2017, 17, 644-651. 19. Cunningham, P. D.; McCreary, K. M.; Jonker, B. T. Auger Recombination in Chemical Vapor Deposition-Grown Monolayer WS2. J. Phys. Chem. Lett. 2016, 7, 5242-5246. 20. Ceballos, F.; Cui, Q.; Bellus, M. Z.; Zhao, H. Exciton Formation in Monolayer Transition Metal Dichalcogenides. Nanoscale 2016, 8, 11681-11688. 21. Chernikov, A.; Ruppert, C.; Hill, H. M.; Rigosi, A. F.; Heinz, T. F. Population Inversion and Giant Bandgap Renomalization in Atomically Thin WS2 Layers. Nat. Photonics 2015, 9, 466-470. 22. Yu, Y.; Yu, Y.; Xu, C.; Barrette, A.; Gundogdu, K.; Cao, L. Fundamental Limits of ExcitonExciton Annihilation for Light Emission in Transition Metal Dichalcogenide Monolayers. Phys. Rev. B 2016, 93, 201111(R). 23. Cunningham, P. D.; McCreary, K. M.; Hanbicki, A. T.; Currie, M.; Jonker, B. T.; Hayden, L. M. Charge Trapping and Exciton Dynamics in Large-Area CVD Grown MoS2. J. Phys. Chem. C 2016, 120, 5819-5826. 24. Sun, Q.-C.; Yadgarov, L.; Rosentsveig, R.; Seifert, G.; Tenne, R.; Musfeldt, J. L. Observation of a Burnstein-Moss Shift in Rhenium-Doped MoS2. ACS Nano 2013, 7, 35063511. 25. Gao, S.; Liang, Y.; Spataruy, C. D.; Yang, L. Dynamical Excitonic Effects in Doped TwoDimensional Semiconductors. Nano Lett. 2016, 16, 5568-5573. 26. Ugeda, M. M.; Bradley, A. J.; Shi, S.-F.; da Jornada, F. H.; Zhang, Y.; Quiu, D. Y.; Ruan, W.; Mo, S.-K.; Hussain, Z.; Shen, Z.-X.; et al. Giant Bandgap Renormalization and Excitonic Effects in a Monolayer Transition Metal Dichalcogenide Semiconductor. Nat. Mater. 2014, 13, 1091-1095. 27. Sim, S.; Park, J.; Song, J.-G.; In, C.; Lee, Y.-S.; Kim, H.; Choi, H. Exciton Dynamics in Atomically Thin MoS2: Interexcitonic Interaction and Broadening Kinetics. Phys. Rev. B 2013, 88. 28. Sun, D.; Rao, Y.; Reider, G. A.; Chen, G.; You, Y.; Brezin, L.; Harutyunyan, A. R.; Heinz, T. F. Observation of Rapid Exciton-Exciton Annihilation in Monolayer Molybdenum Disulfide. Nano Lett. 2014, 14, 5625-5629.


23

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 25

29. Moody, G.; Dass, C. K.; Hao, K.; Chen, C.-H.; Li, L.-J.; Singh, A.; Tran, K.; Clark, G.; Xu, X.; Berghäuser, G.; et al. Intrinsic Homogeneous Linewidth and Broadening Mechanisms of Excitons in Monolayer Transition Metal Dichalcogenides. Nat. Commun. 2015, 6, 8315. 30. Sie, E. J.; McIver, J. W.; Lee, Y.-H.; Fu, L.; Kong, J.; Gedik, N. Valley-Selective Optical Stark Effect in Monolayer WS2. Nat. Mater. 2015, 14, 290-294. 31. Bergren, M. R.; Palomaki, P. K. B.; Neale, N. R.; Furtak, T. E.; Beard, M. C. Size-dependent Exciton Formation Dynamics in Colloidal Silicon Quantum Dots. ACS Nano 2016, 10, 23162323. 32. Steinleitner, P.; Merkl, P.; Nagler, P.; Mornhinweg, J.; Schüller, C.; Korn, T.; Chernikov, A.; Huber, R. Direct Observation of Ultrafast Exciton Formation in a Monolayer of WSe2. Nano Lett. 2017, 17, 1455-1460. 33. Nie, Z.; Long, R.; Sun, L.; Huang, C.-C.; Zhang, J.; Xiong, Q.; Hewak, D. W.; Shen, Z.; Prezhdo, O. V.; Loh, Z.-H. Ultrafast Carrier Thermalization and Cooling Dynamics in FewLayer MoS2. ACS Nano 2014, 8, 10931-10940. 34. Steinhoff, A.; Florian, M.; Rösner, M.; Lorke, M.; Wehling, T. O.; Gies, C.; Jahnke, F. Nonequilibrium Carrier Dynamics in Transition Metal Dichalcogenide Semiconductors. 2D Mater. 2016, 3, 31006. 35. Dery, H. Theory of Intervalley Coulomb Interactions in Monolayer Transition-Metal Dichalcogenides. Phys. Rev. B 2016, 94, 075421. 36. Scharf, B.; Wang, Z.; Van Tuan, D.; Shan, J.; Mak, K. F.; Zutic, I.; Dery, H. Probing ManyBody Interactions in Monolayer Transition-Metal Dichalcogenides. arXiv 2016, 1606.07101v1. 37. Kozawa, D.; Kumar, R.; Carvalho, A.; Amara, K. K.; Zhao, W.; Wang, S.; Toh, M.; Ribeiro, R. M.; Castro Neto, A. H.; Matsuda, K.; et al. Photocarrier Relaxation Pathway in TwoDimensional Semiconducting Transition Metal Dichalcogenides. Nat. Commun. 2014, 5, 4543. 38. Zhu, B.; Cui, X. Exciton Binding Energy of Monolayer WS2. Sci. Reports 2015, 5, 9218. 39. Hichri, A.; Amara, I. B.; Ayari, S.; Jaziri, S. Exciton, Trion and Localized Exciton in Monolayer Tungsten Disulfide. arXiv 2016, 1609.05634. 40. Radisavljevic, B.; Kis, A. Mobility Engineering and a Metal-Insulator Transition in Monolayer MoS2. Nat. Mater. 2013, 12, 815-820. 41. Cabo, A. G.; Miwa, J. A.; Grønborg, S. S.; Riley, J. M.; Johannsen, J. C.; Cacho, C.; Alexander, O.; Chapman, R. T.; Sprigate, E.; Grioni, M.; et al. Observation of Ultrafast Free Carrier Dynamics in Single Layer MoS2. Nano Lett. 2015, 15, 5883-5887. 42. Bertoni, R.; Nicholson, C. W.; Waldecker, L.; Hübener, H.; Monney, C.; De Giovannini, U.; Puppin, M.; Hoesch, M.; Springate, E.; Chapman, R. T.; et al. Generation and Evolution of Spin-, Valley-, and Layer-Polarized Excited Carriers in Inversion-Symmetric WSe2. Phys. Rev. Lett. 2016, 117, 277201. 43. Poellmann, C.; Steinleitner, P.; Leierseder, U.; Nagler, P.; Plechinger, G.; Porer, M.; Bratschitsch, R.; Schüller, C.; Korn, T.; Huber, R. Resonant Internal Quantum Transitions and Femtosecond Radiative Decay of Excitons in Monolayer WSe2. Nat. Mater. 2015, 14, 889-893. 44. Liu, G.-B.; Shan, W.-Y.; Yao, Y.; Yao, W.; Xiao, D. Three-Band Tight-Binding Model for Monolayers of Group-VIB Transition Metal Dichalcogenides. Phys. Rev. B 2013, 88, 085433.


24

Page 25 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

45. Zhou, Y.; Scuri, G.; Wild, D. S.; High, A. A.; Dibos, A.; Jauregui, L. A.; Shu, C.; De Greve, K.; Pistunova, K.; Joe, A. Y.; et al. Probing Dark Excitons in Atomically Thin Semiconductors via Near-Field Coupling to Surface Plasmon Polaritons. Nat. Nanotechnol. 2017, 12, 856-860. 46. Zhang, X.-X.; Cao, T.; Lu, Z.; Lin, Y.-C.; Zhang, F.; Wang, Y.; Li, Z.; Hone, J. C.; Robinson, J. A.; Smirnov, D.; et al. Magnetic Brightening and Control of Dark Excitons in Monolayer WSe2. Nat. Nanotechnol. 2017, 12, 883-888. 47. McCreary, K. M.; Hanbicki, A. T.; Jernigan, G. C.; Culbertson, J. C.; Jonker, B. T. Synthesis of Large-Area WS2 Monolayers with Exceptional Photoluminescence. Sci. Reports 2016, 6, 19159.


25

Photoinduced Bandgap Renormalization and Exciton Binding Energy

Recommend Documents