Observation of Dynamic Screening in the Excited Exciton States in Multi-layered MoS_2
Manobina Karmakar, Sayantan Bhattacharya, Subhrajit Mukherjee, Barun Ghosh, Rup Kumar Chowdhury, Amit Agarwal, Samit Kumar Ray, Debashis Chanda, Prasanta Kumar Datta
OObservation of Dynamic Screening in the Excited Exciton States in Multi-layeredMoS Manobina Karmakar
Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302
Sayantan Bhattacharya
Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302 andpresently at Department of Chemistry, University of Sheffield, Sheffield S3 7HF, United Kingdom
Subhrajit Mukherjee
Advanced Technology and Development Centre, Indian Institute of Technology Kharagpur, Kharagpur, India 721302 andpresently at Faculty of Materials Science & Engineering,Technion – Israel Institute of Technology, Haifa, Israel - 3203003
Barun Ghosh
Department of Physics, Indian Institute of Technology - Kanpur, Kanpur 208016, India
Rup Kumar Chowdhury
Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302
Amit Agarwal
Department of Physics, Indian Institute of Technology - Kanpur, Kanpur 208016, India
Samit Kumar Ray
Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302 andS. N. Bose National Centre for Basic Sciences, Kolkata, India 700106
Debashis Chanda ∗ NanoScience Technology Center, Department of Physics and CREOL,The College of Optics and Photonics, University of Central Florida, Orlando, FL 32826, USACREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816 andDepartment of Physics, University of Central Florida, Orlando, FL 32816, USA
Prasanta Kumar Datta † Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302
Excitonic resonance and binding energies can be altered by controlling the environmental screeningof the attractive Coulomb potential. Although this screening response is often assumed to be static,the time evolution of the excitonic quasiparticles manifests a frequency-dependence in its Coulombscreening efficacy. In this letter, we investigate a ground (1s) and first excited exciton state (2s) ina multi-layered transition metal dichalcogenide (MoS ) upon ultrafast photo-excitation. We explorethe dynamic screening effects on the latter and show its resonance frequency is the relevant frequencyat which screening from the smaller-sized 1s counterparts is effective. Our finding sheds light onnew avenues of external tuning on excitonic properties. Excitons or Coulomb-bound electron-hole pairs insemiconductors possess a potential for faster optical com-munication due to the efficient light-matter couplingand higher packing density compared to conventionalelectronics[1, 2]. The fundamental interaction that al-ters the bound state of an electron-hole pair is screen-ing or attenuation of the Coulomb potential in pres-ence of neighboring charge carriers which includes butnot limited to atoms (dielectric screening), free carriers,excitons, and plasma. Enhanced screening leads to re-duced exciton oscillator strength (OS) and binding en-ergy (BE)[3, 4]. A plethora of experimental studies uti- lize this ubiquitous phenomenon to realize external con-trol of the excitonic states through photo-excitation[5],carrier-injection[4], and modification of the dielectricenvironment[6–9]. However, the theoretical formulationsthat account for screening quantitatively are long-soughtand well-debated[10–13]. While many of the previousstudies consider long-wavelength (static) response of theenvironmental macroscopic polarization to account forthe experimental results, static approximation largelyoverestimates the screening efficiency of the quasiparti-cles leading to inconsistencies between experimental andtheoretical binding energies, oscillator strengths, Mott a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b density etc.[13, 14] The sole reason is that static polar-ization responses from the surrounding charge-carryingparticles are too slow to screen the excitonic Coulombfield that evolve at much faster time-scales[13].The excitons are continuously annihilated and recre-ated through exchange interactions[15] and scatteredto free-carriers[16–18]; therefore, the Coulomb potentialthat binds the excitons is not static in time. Some recenttheoretical studies indicate certain ”characteristic fre-quencies” at which exciton screening is predominant[13,19]. Nevertheless, one major bottleneck in the under-standing of the dynamic nature of Coulomb screeningis the severe lack of experimental evidence. Therefore,the characteristic frequency (or frequencies) is an openquestion to date. Apart from clarity in the underlyingphysics, an effective device engineering necessitates com-prehension of the dynamic screening effects in excitons.Motivated by this, we explore the free-carrier andexciton-induced screening effects in excitons using ultra-fast transient absorption spectroscopy that allows us toprobe the temporal evolution of the screening. We choosemulti-layered Molybdenum di-sulfide (MoS ), a widelystudied transition metal dichalcogenide (TMDC) mate-rial that offers stable, room-temperature excitons, whichare also prone to sizable Coulomb screening owing tothe layered architecture[20]. We track the photo-inducedevolution of the ground (1s) and first excited (2s) exci-tonic states. Despite expected photo-bleaching like 1sstate, we observe an enhancement in the 2s exciton ab-sorption oscillator strength followed by photo-excitation.We model the excitation-induced changes in the intrinsicdielectric permittivity (DEP) and reveal a reduction inthe frequency-dependent (dynamic) dielectric permittiv-ity of the 2s state, which triggers the enhanced absorp-tion in the particular state. Precisely, the 2s excitonsare sensitive to the intrinsic DEP dictated by 1s excitonsat the 2s resonant frequency. This observation providesfirst-ever experimental evidence towards the perceptionof exciton-induced dynamic screening in semiconductors.Linear absorption spectrum of sono-chemically ex-foliated multi-layered MoS [21] (Supplemental Mate-rial(SM) S1-S2) depicts the well-known A and B exci-tonic features centered around 675 nm (1 .
84 eV) and 614nm (2 .
02 eV). Quasiparticle bandstructure calculations(SM,S3) of the multi-layered TMDC using GW methodis presented in Fig. 1(a).We study ultrafast transient absorption spectra ofMoS flakes obtained using a 415 nm (2 .
98 eV) pumpexcitation and a CaF generated broadband supercon-tinuum probe pulse and a variable pump-probe delay upto 3 ns. A schematic illustration of the light-matterinteraction is depicted in Fig. 1(b). Fig. 1(c) revealsthe background-corrected transient probe absorbance(SM,S5) or A pump ( λ ), at a few selected probe delays (0.2 -0.7 ps) and that without pump-excitation (-10 ps). Withincreasing probe delay, we observe red-shifted A and B absorption along with an aberrant distortion in the spec-tral shape of each exciton at the higher energy side. Toresolve any small spectral features, we plot the second-derivative of the absorption data in Fig. 1(d). The deriva-tive spectrum at -10 ps delay looks symmetric, whereas,at higher delays, the spectrum deviates significantly atthe lower wavelength side of each exciton. This observa-tion indicates appearance or enhancement of additionalfeatures other than the A and B ground states followedby photo-excitation. The possibility of observing higher-order quasiparticles (trions or bi-excitons) are precluded,as they lie on the higher wavelength side of the excitonicfeatures[22]. A possible artifact of photo-induced lat-tice heating is the appearance of phonon sidebands[23].We perform temperature-dependent linear absorption toidentify phonon sidebands at an elevated temperature(Fig. S2.2, SM). However, no asymmetry or kink appearsat the higher-energy side of each exciton. The possibil-ity of interlayer excitons is also ruled out(SM, S11)[24–26]. Consequently, we assign these new features to thefirst excited states of excitons (2s excitonic states)(alsosee SM,S12). We fit the derivative spectrum of the ab-sorption data in the absence of pump and identify the2s states of A excitons centered around 648 nm (1 . ∼ / . ± .
007 eV of A,1s excitons [28, 29].Recent reports on bulk and multi-layered TMDC[30, 31]estimate similar values.Temporal behavior of the various parameters includ-ing exciton oscillator strength (OS), energy resonance,linewidth, 1s-2s energy separation are found by fittingthe second-order derivative (with respect to wavelength λ ) of transient probe absorbance with the second-orderderivative of the Gaussian-convoluted Elliott formula [27]in equation 1. d A pump ( λ ) dλ = d dλ (cid:88) i = A,B (cid:88) j =1 s, s A ij Γ ij e − h c ij (cid:16) λ − λij (cid:17) . (1)Here, A ij is the normalized amplitude of the Gaussian(oscillator strength), Γ ij is the linewidth and λ ij is theexciton peak wavelength. Fig.S6 in SM explicitly showsthe excellent fitting of Eq. 1 with the data by retainingonly the 1s and 2s excitons for the A and only 1s excitonsfor B resonances. Extracted parameters for both groundand first excited states of A exciton for varying probe-delays are presented in Fig. 1(e). The oscillator strength A s corresponding to 1s state shows reduction suggest-ing Pauli-blocking and screening due to pump-inducedquasiparticles[32]. We observe two exponential decaycomponents τ ( ∼ ps) and τ ( ∼ ns) dictate the dynamicsand are assigned to non-radiative carrier scattering[33]and radiative exciton recombination[34–36], respectively(SM,S7). In contrast to the 1s state, we find an enhanced FIG. 1. (a)Quasiparticle bandstructure of 20-layered MoS . (b) Schematic of the multi-layered, dispersed TMDC and ultrafastlight-matter interaction. (c) Absorbance [A pump ( λ )] of multi-layered MoS flakes at different probe delays for a pump-fluenceof 11 µ J/cm , showing the A and the B exciton resonance (d) The second-derivative of A pump ( λ ) (with respect to λ ) at differentprobe delays. The inset shows a schematic of the 1s and 2s excitonic states of both A and B resonances. (e) Temporal-evolutionof various excitonic parameters related to ground and first excited state of A exciton, namely exciton oscillator strength,resonance energy, 1s-2s resonance energy separation, and exciton linewidth under above-bandgap pump-excitation. absorption OS for the 2s state, which eventually reversesto the steady-state value after a few ns. Such absorp-tion enhancement indicates an effective increase in BErather than Pauli-blocking of the particular state. Wewill discuss this in detail.Pump-induced charge carriers renormalize the repul-sive potential energy (self-energy) and reduce the single-particle bandgap, leading to a lowering of the excitonresonance energies ( δ r )[4, 32, 37]. Simultaneously, thescreening of the attractive interaction between the exci-ton constituents, reduces its BE, making it blue-shiftedtowards the conduction band edge: E j → E j − δ r + δ b | j , where E j = hcλ j , j = 1 s, s [37]. For a locally-screened Coulomb potential, δ b | s > δ b | s [28](SM,S10).Consequently, a higher red-shift in the 2s state is ob-served. Moreover, the excitonic linewidth is narrowedby 24 meV, followed by the pump-excitation. A plau-sible reason is the increase in the exciton coherencelifetime owing to Pauli-blocking of the momentum-darkstates[38, 39](SM,S8).Having an overall idea on the time-evolution of theexcitonic properties, we turn to investigate the screeningand 2s exciton OS enhancement. Locally-screened, three-dimensional Hydrogen model[28] describes the tuning ofCoulomb interaction of an electron-hole pair by employ-ing an effective DEP experienced by the excitons for n th state: (cid:15) r | n = µe (4 π(cid:15) ) (cid:126) n E b | n . (2)Where, E b | n is exciton BE of n th exciton state, µ is exci-ton effective mass and (cid:15) r | n is effective dielectric constant.This quantity (cid:15) summarizes all Coulomb screening effectsexperienced by an electron-hole pair[29]. If we consideran oversimplified picture of an exciton, where an electronand hole pair is a static entity in real space and time, thestatic DEP of the environment will describe the screeninginteractions sufficiently. However, different many-bodyinteractions take place that continuously abolish and cre-ate the Coulomb pairs. For instance, excitons get ionizedto free carriers through phonon-interactions, annihilatedand recreated through exchange interactions, scatteredto momentum-dark states upon phonon-interactions, etc.Each of these processes have their specific time-scales.For example, exchange interaction happens at the fre-quency of the excitonic resonance; exciton ionization hap-pens at the frequency related to the BE of the excitons.Accordingly, the medium surrounding an exciton screensthe electron-hole interactions at those particular frequen-cies. Polarizability response of the environment at otherfrequencies are either too slow or too fast to affect theCoulomb interactions significantly.In the case of an ideal two-dimensional semiconduc- FIG. 2. (a) Temporal evolution of 1s-2s resonance energy separation (∆ ) and the absorption oscillator strength of 2s excitons(A s ). (b) (Left) A pedagogical, schematic illustration of the effectiveness of the screening (W( ω )) and DEP ( (cid:15) r ( ω )) of MoS over a broad energy range. The dielectric function below 10 − eV is dominated by phonons (Ph), inter-excitonic transitions(Int. Ex.), and plasma, whereas excitons (Ex.) dominate the spectrum at few eV range. (Right) A schematic of the 1s(red-blue circle) and 2s excitons (purple-yellow circles). Field lines joining the latter penetrates the smaller 1s excitons whichcontribute to screening. (c)Exciton-induced permittivity of 20-layered MoS estimated using Kramers-Kronig relations. (d)Temporal variation of the DEP of MoS at the 2s resonance. (e) Temporal variation of 2s state OS for different pump-fluences.Experimentally obtained values (same as (a)) are presented as scatter plots, and the solid lines are the estimated values fromequation 2 and 4. (f) Similar to (e), with minimized mean-squared error with respect to scaling of A and B, 1s absorption OS. tor, the environmental screening of an exciton includesthe substrate-response and a minimal response from thesemiconducting layer itself. For a three-dimensional sys-tem like the one we study, the field-lines joining an elec-tron and a hole are essentially within the same material.Hence, the screening of the Coulomb field is predomi-nantly from the surrounding layers.In our experiments, pump-induced excitons and carri-ers modify the charge environment of the 2s excitons suchthat its effective permittivity is reduced and OS is en-hanced. Although we consider the dynamic screening inthe TMDC, it is almost an improbable task to determinethe effectiveness of the screening at each frequency ofthe electromagnetic spectrum. However, as we discussedearlier, some particular frequencies (resonance frequency,binding energy/ (cid:126) ) are more effective than the other. InFig. 2(b), we sketch the frequency-dependent effective-ness (W( ω )) and the environmental (intrinsic) DEP forpedagogical purpose; we estimate the effective permittiv-ity of an excitonic state by (cid:15) r | n = (cid:82) ∞ W ( ω ) (cid:15) r ( ω ) dω (cid:82) ∞ W ( ω ) dω (3) It is evident that static dielectric permittivity increasesdue to the pump-induced elevated population of chargecarriers. Also, the plasma frequencies owing to the carrierinjection is estimated at ∼ − meV, much less than the2s exciton BE. Therefore, the effective permittivity of 2sstates reduces neither at static limits nor at the bindingenergy range. The remaining frequency of interest is theresonance of the 2s state.We present the delay-dependent 1s-2s resonance en-ergy separation (∆ ) and A s in Fig. 2(a) for four dif-ferent pump-fluences. Notably, the non-monotonic dy-namics of A s and ∆ seem to be inversely correlated,with the maxima in A s temporally coinciding with theminima in ∆ . This observation reaffirms the existenceof strong dynamic screening. Consequently, we trace thetime-dependent intrinsic DEP of MoS at the 2s reso-nance energy.Following equation 2 and calculated exciton reducedmass of 0 . m , we extract the effective steady-stateDEP of 5 .
7. We separate the effective DEP of the 2sexcitons into two components-(i)permittivity at excitonresonance due to 1s excitons (ii) a core DEP due to otherinterband transitions as a cumulative effect from all fre-
FIG. 3. Second-order derivative of the TA spectra at a fewselected delays after photo-excitation with (a) 500 nm and(b) 800 nm pump of fluence of 6 µ J/cm and 264 µ J/cm ,respectively. quencies other than the resonance. While the first termevolves with photo-excitation, the other is assumed to befixed. This assumption serves our purpose of investigat-ing the variation of screening at the resonance.We employ Kramers-Kronig (KK) relation[40] basedon the linear absorbance data in the visible region (SM,S9) to find out (i), i.e., the real part of the dielectricdispersion ( (cid:15) r, KK ( λ )= (cid:15) r − (cid:15) core ) due to excitons. Notethat material permittivity is given by (cid:15) r, KK ( λ ) + (cid:15) core ,where (cid:15) core is a nearly frequency-invariant backgroundpermittivity originating from interband transitions. Aswe use TMDC flakes in dispersion, with probe beam size( ∼ µ m beam-diameter) being few-orders larger thanthe individual suspended flakes, the experimentally mea-sured absorbance is less than the actual absorbance of a20-layered MoS flake. Therefore, we estimate a scalingparameter (5 ±
2) of the absorbance by extrapolating anearlier work[9] (see SM,S9). Next, we plot the exciton-induced DEP with (for probe-delay of 0.5 ps) and with-out photo-excitation in Fig. 2(c) using the correspondingexperimentally obtained ∆ values in KK equation. Ascompared to the un-pumped condition, a reduction inthe DEP at the 2s exciton resonance is comprehensible.We note that the exciton OS ( A j ) in a three dimensionalsemiconductor varies as A j ∝ r − j , where r j denotes theexciton radius[40]. The exciton radius, in turn, varieslinearly with the effective DEP[41], leading to A j ∝ (cid:15) − r . (4)Thereafter, we calculate the delay-dependent reductionin (cid:15) r | s and accordingly find A s at different probe delay(Fig.2 (d) and (e)). Remarkably, the temporal evolutionof the A s is well-reproduced qualitatively. However, cal-culated values underestimate experimental A s , almostby a factor of . This is improved by optimizing the scal-ing parameter by 40 %, which lies within the standarderror of the mentioned data extrapolation. Re-calculatedA s values displayed in Fig. 2(f) depicts a better quanti-tative estimation of the experimental data. This observa-tion excellently demonstrates the screening of 2s excitonsdue to the smaller-sized 1s excitons. Photo-excitationtriggers reduced effective permittivity due to reduced 1s- 2s energy separation, which facilitates reduced screeningor ”antiscreening”[42] leading to the enhanced excitonOS. This effect has an upper-limit pertaining to the 2sexciton resonance entering anomalous dispersion regionof 1s exciton oscillator(SM,S10).We repeat the pump-probe experiments with thin-filmsof multi-layered flakes on quartz substrates. We excitethe sample linearly with 500 nm and 800 nm pump andobserve the resulting second-derivative of the transientabsorption in Fig.3. The 800 nm pumping condition con-stitutes an interesting case where A,1s excitons do notform. Therefore, in contrast to the 415 nm and 500 nmpumping, the kinks owing to the enhanced 2s excitonicfeatures do not appear for 800 nm pump and therebyre-affirms the role of 1s excitons in 2s exciton screening.In this letter, we provide a strong experimental evi-dence of dynamic Coulomb screening in excitons and re-veal that environmental polarization response at its res-onance effectively controls the screening and hence theabsorption strength of the excitons. We observe that de-spite the presence of photo-induced carriers that induceincreased static-screening, 2s exciton absorption is en-hanced. We reproduce this aberrant experimental obser-vation by considering the intrinsic dielectric permittivityat its resonance owing to the 1s excitons. 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