Two-Dimensional Plasmonic Polarons in N-Doped Monolayer Mos2

Two-dimensional plasmonic polarons in n -doped monolayer MoS2

Item Type Article

Authors Caruso, Fabio; Amsalem, Patrick; Ma, Jie; Aljarb, Areej; Schultz, Thorsten; Zacharias, Marios; Tung, Vincent; Koch, Norbert; Draxl, Claudia

Citation Caruso, F., Amsalem, P., Ma, J., Aljarb, A., Schultz, T., Zacharias, M., … Draxl, C. (2021). Two-dimensional plasmonic polarons in n - doped monolayer MoS2. Physical Review B, 103(20). doi:10.1103/ physrevb.103.205152

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DOI 10.1103/physrevb.103.205152

Publisher American Physical Society (APS)

Journal Physical Review B

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Download date 29/09/2021 17:17:36

Link to Item http://hdl.handle.net/10754/669060 Two-dimensional plasmonic polarons in n-doped monolayer MoS2

Fabio Caruso,1, 2 Patrick Amsalem,2 Jie Ma,2 Areej Aljarb,3 Vincent Tung,3, 4 Norbert Koch,2, 5 and Claudia Draxl2 1Institut fürTheoretische Physik und Astrophysik, Christian-Albrechts-Universitätzu Kiel, D-24098 Kiel, Germany 2Institut fürPhysik and IRIS Adlershof, Humboldt-Universitätzu Berlin, Berlin, Germany 3Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia 4Molecular Foundry Division, Lawrence Berkeley National Lab, Berkeley, CA, USA 5Helmholtz-Zentrum fürMaterialien und Energie GmbH, Berlin, Germany (Dated: June 29, 2020) We report experimental and theoretical evidence of strong electron-plasmon interaction in n- doped single-layer MoS2. Angle-resolved photoemission spectroscopy (ARPES) measurements reveal the emergence of distinctive signatures of polaronic coupling in the electron spectral function at energies that are not compatible with a coupling mechanism due to polar optical phonons. Our first- principles calculations based on many-body perturbation theory illustrate that electronic coupling to photo-excited two-dimensional (2D) carrier plasmons provides an exhaustive explanation of the experimental spectral features and their energies. These results constitute compelling evidence of the formation of plasmon-induced polaronic quasiparticles, suggesting that highly-doped transition- metal dichalcogenides may provide a new platform to explore strong-coupling phenomena between electrons and plasmons in 2D.

The interplay of charge confinement, reduced dielec- ficulty to achieve degenerate doping concentrations (nec- tric screening, and strong light-matter coupling in few- essary for the emergence of well defined plasmon reso- layer semiconducting transition-metal dichalcogenides nances), while simultaneously retaining crystallinity of (TMDCs) underpins a vast spectrum of emergent many- the sample. Single-layer TMDCs circumvent these prob- body effects, including the formation of excitons [1–4], lems: (i) the 2D confinement of plasmons and charge car- trions [5], polarons [6, 7], polaritons [8–12], and supercon- riers sets the ground for the establishment of a strong- ductivity [13]. At variance with three-dimensional solids, coupling regime and (ii) highly-tunable carrier density TMDCs further allows for unprecedented opportunities can be realized. In particular, some of us have recently to tailor these phenomena via cavity embedding [14], cir- demonstrated that the carrier population in the conduc- cular dichroism [15, 16], gating [13], nano-structuring tion band of monolayer MoS2 and WS2 can be tailored [12, 17], substrate engineering [18], and doping [6]. by stimulating the formation of chalcogen vacancies via Highly-tunable carrier densities are particularly desir- repeated annealing cycles [29]. able for the study of many-body interactions in TMDCs, Here, we report the observation of plasmon-induced as they may enable control of plasmons (collective exci- polarons in n-doped monolayer MoS2. ARPES mea- tation of the electron density) and polarons (electrons surements of the conduction band of MoS2 reveals the dressed by a phonon cloud) [19, 20]. Polarons typi- emergence of distinctive fingerprints of bosonic satellites cally arise in semiconductors and insulators as a result of due to electron-boson coupling. The boson energy of strong coupling to longitudinal-optical (LO) vibrational ∼ 170 meV is much larger than the characteristic phonon modes [19–22]. The formation of polarons may lead to energies in MoS2 (~ω < 60 meV), and it is thus incompat- charge trapping [21, 23] and to a renormalization of the ible with a coupling mechanism due to LO phonons. By band effective masses [22]. The relevance of such phe- explicitly accounting for the effects of electronic coupling nomena for the opto-electronic properties of solids, along- to 2D plasmons in a first-principles many-body frame- side with the recent discovery of polarons in the photoe- work, our calculations of the spectral function identify mission spectrum of doped oxides [19, 20] and 2D mate- electron-plasmon interactions as the origin of the pola- rials [6, 24], has reignited theoretical and experimental ronic spectral features observed in experiments. These research on polaronic quasiparticles [7, 21–23, 25–28]. findings provide compelling evidence of the emergence of In close analogy to phonon-induced polarons, recently 2D plasmonic polarons in n-doped monolayer MoS2, and discovered in n-doped bulk MoS2 [6, 7], the formation of they demonstrate the establishment of a strong-coupling polaronic quasiparticles may also be stimulated by the regime resulting from the confinement of carriers and coupling to extrinsic plasmons [25], and may lead to the plasmons in 2D. emergence of polaronic satellites in angle-resolved pho- The measured sample consists of a chemical-vapor- toemission spectroscopy (ARPES) experiments. The ex- deposition (CVD) grown fully-closed MoS2 monolayer perimental observation of plasmonic polarons in three- film on a sapphire substrate [30]. Top mechanical clamp- dimensional solids is hindered by rather low electron- ing of the sample enabled electrical contact of the mono- plasmon coupling strengths (λ ≤ 0.5 [25]), and by the dif- layer to ground. Sample charging during ARPES mea- 2

13 −2 and n2 = 4 · 10 cm (referred to simply as n1 and n2 in the following), respectively, whereas the full measured spectral function for the valence band is shown in Supplementary Fig. S1 [34]. The on-curve labels indicate the photo-electron crystal momentum ∆k = k − kK, relative to the K point in units of A.˚ Energies are referenced to the Fermi level that is located 39 and 56 meV above the conduction-band minimum (CBm), respectively. At K and neighboring crystal momenta, the spectral functions are characterized by a quasiparticle peak close to the Fermi level. The peak position corresponds to the binding energy of quasi-electrons around the CBm. At binding energies larger than those of quasiparticle excitations, the spectral function for carrier concentration n1 (n2) exhibits a shoulder-like structure red-shifted by 100 meV (170 meV) from the quasiparticle peak and ex- Figure 1. (a) Spectral signatures of plasmonic polarons in tending up to 0.6 eV below the Fermi level. These spec- the ARPES spectral function of n-doped MoS2 for carrier 13 13 −2 tral features, indicated by arrows in Figs. 1 (a) and (b), densities n1 = 2.8·10 (a) and n2 = 4·10 cm (b). Labels indicate the photo-electron crystal momentum relative to the become more pronounced at higher carrier densities. For K point (∆k = k − kK) along K-Γ in units of A,˚ and satellite a small momentum offset from the K point (∆k = 0.06 A)˚ features are indicated by arrows. Energies are relative to the a well-defined peaked structure can be resolved, as shown Fermi level. ARPES measurements (dots) and first-principles in Supplementary Fig. S2 [34]. calculations (red) of the spectral function at K for n1 (c) A more detailed view of these spectral signatures is and n2 (d). Vertical dashed lines mark the positions of the first and second satellite peaks in the calculated spectra. The given in Figs. 1 (c) and (d), which report the spectral fit (dark blue) of the experimental spectra and its spectral functions for n1 and n2 (corresponding to the thick lines decomposition as Gaussian lineshapes (shaded curves) are a in Figs. 1 (a) and (b)) measured with longer acquisition guide to the eye. times for improved signal-to-noise ratio. For n2, the spectral function exhibits a satellite structure at 170 meV and a less-pronounced secondary structure at 330 meV below the quasiparticle peak. These features, also visible surements was avoided upon doping of the monolayer as in Fig. S2 for ∆k = 0.06 A,˚ closely resemble the char- described thereafter. Degenerate n-doping was achieved acteristic spectral fingerprints of electron-boson interac- by repeated in-situ vacuum annealing cycles (with final tion in photoemission spectroscopy. Specifically: (i) they annealing for 12 hours at 850 K), which is known to ef- have non-vanishing intensity within the gap and, there- fectively n-dope MoS2 monolayer films from field-effect- fore, may not be attributed to the emission of a photo- transistor characterization [31]. Doping results from the electron; (ii) they are roughly spaced from the quasipar- formation of sulfur vacancies either by direct desorption ticle peak by multiples of ~Ω =170 meV, as illustrated of sulfur atoms or by desorption of substitutional oxy- by the spectral-function decomposition in terms of Gaus- gen present at sulfur-vacancy sites, naturally present in sian lineshapes shown in Figs. 1 (b) and (c). These points CVD grown samples [32, 33]. The photoemission mea- suggest that carriers in the conduction band may be sub- surements were performed in an analysis chamber (base ject to polaronic coupling to bosonic excitations – such pressure 2 · 10−10 mbar) equipped with a Specs Phoi- as, e.g., polar phonons or 2D carrier plasmons – and that bos 100 hemispherical electron analyzer and using the the first and second satellites may stem from the excita- HeI radiation provided by monochromated helium dis- tion of one and two bosons with an effective energy ~Ω charge lamp (consisting of a HIS-13 lamp mounted on alongside with the creation of a photo-hole. a VUV5046 UV-monochromator). All the measurements The comparison between the boson energy ~Ω and the were performed at room temperature. The overall energy energy of optical phonons in MoS2, that ranges between resolution amounted to 117 meV (65 meV instrumental between 30 and 60 meV, as illustrated in Supplementary energy resolution) as determined from the Fermi edge of Fig. S3 [34], allow us to promptly exclude the Fröhlich in- a polycrystalline gold sample and the angular resolution teraction between electrons and LO phonons as possible was about ±2 degrees. The energy distribution curves coupling mechanism responsible for the satellite forma- were measured every two degrees by rotating the manip- tion. Recent experimental and theoretical investigations ulator about the polar axis. of bulk MoS2 [6, 7] have indeed revealed the emergence Figure 1 (a) and (b) report ARPES spectral functions of Holstein polarons in ARPES. However, their spectral of MoS2 for crystal momenta in the vicinity of the K high- signatures occur at 30-40 meV below the Fermi energy, 13 symmetry point for doping concentrations n1 = 2.8 · 10 energies that are too small to possibly explain the pola- 3

where me is the bare electron mass. This approximation is justified by the highly-isotropic dispersion of the conduction band at the K point and by comparison between the conduction band of MoS2 and the parabolic-band dispersion of the 2HEG in Fig. 2 (a). We further explicitly account for the extrinsic dielectric environment induced by the semi-infinite sapphire (Al2O3) substrate by intro- S Al2O3 ducing the dielectric constant ∞ = (1 + ∞ )/2 = 6.3, Al2O3 with ∞ ' 11.6 being the high-frequency dielectric constant of bulk sapphire [39]. The loss function, illustrated in Fig. 2 (b) for the carrier concentration n2, exhibits pronounced plasmon peaks, with plasmon energies ωpl(q) ranging from 0 to Figure 2. (a) Conduction band of MoS2 obtained from ~ density-functional theory (blue), and dispersion of a 2D ho- 0.3 eV. Only plasmons with momenta |q| < qc can be −1 mogeneous electron gas with effective mass m∗ = 0.86 (red). excited, where qc ' 0.18 A˚ (marked by a dashed ver- The dashed horizontal lines mark the position of the Fermi tical line in Fig. 2 (b)) is the critical momentum for the level F for the carrier concentration n2. Energies are refer- onset of Landau damping, namely, the decay of plasmons enced to the conduction-band minimum. (b) Loss function upon excitation of electron-hole pairs. The plasmon dis- and plasmon dispersion of n-doped MoS2 for the carrier con- persion obtained from the loss function compares well centration n . The vertical dashed line marks the critical 2 with the analytical result for homogeneous 2D metals [40] momentum cutoff q corresponding to the onset of Landau c pl p ∗ S damping for 2D plasmons. The continuous line illustrates the ωq = 2πnq/m ∞ (1 + 3q/8) , illustrated in Fig. 2 (b) plasmon dispersion. as a continuous line. At first, the broad energy range covered by the plasmon dispersion (0-300 meV) may seem incompatible with the satellite features observed in ARPES, which suggest ronic spectral features of Fig. 1. In analogy to polarons in a coupling to a single bosonic excitation with energy oxides [27], strong coupling between electrons and plas- ~Ω = 170 meV. To show that the plasmon dispersion mons may also trigger the formation of plasmon-induced may actually give rise to spectral signatures of bosonic polaronic quasiparticles (plasmonic polarons) in n-doped coupling with a well-defined energy, we consider the den- semiconductors and insulators. Plasmonic polarons re- sity of states of plasmonic excitations: sult from the simultaneous excitation of a plasmon and Z −1 pl a hole and they manifest themselves in ARPES under J(ω) = ΩBZ dqδ(ω − ωq ) = κωθ(ωc − ω) (1) the form of photoemission satellites. To inspect whether ΩBZ a bosonic coupling mechanism induced by carrier plas- where κ = 2m∗S (Ω n)−1 and ω = ωpl is the plasmon ∞ BZ c qc mons may account for these phenomena, we proceed to energy at the critical momentum qc. This result may be investigate the plasmon dispersion in doped MoS2. promptly verified by analytical integration of Eq. (1) by For concentrations of n-type carriers larger than 1 · retaining only the leading order term in the plasmon dis- 13 −2 pl 10 cm , MoS2 undergoes a Mott’s metal-insulator persion ωq in the long-wavelength limit (q → 0). From transition [35], characterized by the onset of metallic Eq. (1), we can estimate the average plasmon energy as ω = R J(ω)ωdω[R J(ω)dω]−1 = 2 ω /3 and the stan- transport properties [36] and by the partial filling of the ~ ~ ~ c √ 2 2 1/2 K valley in the conduction band. The conduction-band dard deviation σ = ~(ω − ω ) = ~ωc/ 18 ' 0.24~ωc. dispersion as obtained from density-functional theory cal- For n2, the value ~ωc ' 0.3 eV yields ~ω = 200 meV culations is reported in Fig. 2 (a). The Fermi energy of which agrees well with the effective boson energy ~Ω = the doped system depends linearly on the carrier concen- 170 meV derived from the satellite energy. Similarly, 2 ∗ tration n via the expression F = π~ n/m Nv − ECBm, the standard deviation σ = 0.07 eV is in good agreement with Nv = 2 being the K-valley degeneracy, and ECBm with the half width at half maximum of the satellite peak the energy of the CBm. For the carrier concentration n1 ∆w = 90 meV, which we extract from Gaussian decom- and n2 this expression yields F = 39 and 56 meV, re- position of the experimental spectra. This analysis sug- spectively. The latter value is marked by the horizontal gests that the energies and linewidths of the satellites are dashed line in Fig. 2 (a). Upon interaction with light, ex- compatible with a bosonic coupling mechanism induced trinsic carriers in the conduction band can be collectively by 2D carrier plasmons. excited leading to well-defined 2D carrier plasmon reso- To quantitatively demonstrate the influence of the nances. The energy-momentum dispersion relation of 2D electron-plasmon interaction on ARPES measurements, plasmons in MoS2 is here approximated by the loss func- we conducted first-principles calculations of the spectral tion L(ω) = Im [(q, ω)]−1 of a 2D homogeneous electron function based on the cumulant expansion approach [41– ∗ gas (2HEG) [37, 38], with effective mass m = 0.86 me, 43], the state-of-the-art for spectral-function calculations 4 of coupled electron-boson systems [44]. The cumulant spectral function can be expressed as [22]:

S X Ank(ω)∗ QP A(k, ω) = e Ank (ω) (2) n where ∗ denotes convolution over frequency, and QP −1 −1 Ank (ω) = 2π Im [~ω − εnk − Σnk(εnk)] is the quasiparticle contribution to the spectral function, εnk is the single-particle energy, and Σ is the electron self-energy due to the electron-plasmon interaction, for which an ex- plicit expression is given in the Supplemental Material [34]. Dynamical correlations due to the electron-plasmon interaction are accounted for by the satellite function S Figure 3. (a) First-principles calculations of the angle- Ank: resolved spectral function of MoS2 at the K point for a carrier concentration n = 4 · 1013 cm−2. (b) Inﬂuence of ﬁnite en- β(ω) −β(ε/~) −(ω − ε/~)(∂β/∂ω)| AS(ω) = ε/~ , (3) ergy and momentum resolutions on the angle-resolved spec- (~ω − ε)2 tral function. (c) ARPES measurements.

1 with β(ω) = π Im Σ(ε/~ − ω)θ(µ/~ − ω), and the depen- dence on n and k has been omitted [45]. scattering. Scattering between plasmons and phonons The cumulant spectral function of n-doped MoS is il- 2 can indeed lower the plasmon lifetime, introducing addi- lustrated in Fig. 1 (c)-(d) as a red line for n and n , 1 2 tional broadening of the plasmon satellite [38]. respectively. The experimental background signal has been added to theoretical data to facilitate the compar- In conclusion, we reported the observation of 2D plas- ison. The calculated spectral function exhibits two dis- monic polarons in n-doped monolayer MoS2 at degener- tinct satellite resonances at energies in excellent agree- ate doping concentrations. The emergence of distinctive ment with the ARPES spectral features. The Taylor ex- signatures of polaronic satellites in ARPES experiments pansion of Eq. (2) up to second order in AS promptly provides compelling evidence of the strong coupling be- reveals the physical origin of these spectral features: between 2D carrier plasmons and extrinsic carriers, and side the quasiparticle peak, arising from AQP alone, the it is corroborated by first-principles calculations of the second term in the expansion stems from the convolution electron-plasmon interaction. This finding indicates that, AS ∗ AQP, and its intensity may be attributed to the rate at sufficiently large doping concentrations, the quantum of photoemission processes resulting from the coupled ex- confinement of holes and plasmons in a 2D semiconductor citation of a photo-hole and a plasmon. Similarly, subse- triggers the onset of a strong-coupling regime, whereby quent arguments in the Taylor expansion can be related electron-plasmon coupling results in the formation of 2D to multiple plasmon excitations. This allows us to relate plasmonic polarons. subsequent satellites to photoemission processes resulting FC acknowledges useful discussions with Pasquale from the simultaneous excitation a photo-hole and emis- Pavone. This work was funded by the Deutsche sion of plasmons. At variance with polaronic satellites Forschungsgemeinschaft (DFG) – Projektnummer due to the electron-phonon interaction, the energy of the 182087777 – SFB 951. satellite peak cannot be related to a single bosonic exci- AA, and VT are indebted to the support from the KAUST tation, but rather to the first moment of the plasmonic Office of Sponsored Research (OSR) under Award No: density of states. However, plasmons can still be emit- OSR-2018-CARF/CCF-3079. ted across the whole energy range covered by the plasmon dispersion, resulting in a broadening of the plasmon [1] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 105, 136805 (2010). peak. The quantitative agreement between experiment [2] D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Phys. and theory is further illustrated in Fig. 3, where the cal- Rev. Lett. 111, 216805 (2013). culated and measured angle-resolved spectral functions [3] A. Molina-Sánchez, M. Palummo, A. Marini, and are compared for the whole CBm. Finite experimental L. Wirtz, Phys. Rev. B 93, 155435 (2016). resolution for energy (momentum) is explicitly accounted [4] J. Hong, R. Senga, T. Pichler, and K. Suenaga, Phys. for in Fig. 3 (b) by convolution with a Gaussian function Rev. Lett. 124, 087401 (2020). with full-width at half maximum of 100 meV (0.1 A˚−1). [5] K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F. Heinz, and J. Shan, Nature Mater. 12, 207 (2013). The calculated satellite structure is slightly more pro- [6] M. Kang, S. W. Jung, W. J. Shin, Y. Sohn, S. H. Ryu, nounced as compared to measurements, since our calcula- T. K. Kim, M. Hoesch, and K. S. Kim, Nature Mater. tions do not explicitly account for finite lifetime effects in 17, 676 (2018). the plasmon dispersion arising from the plasmon-phonon [7] P. Garcia-Goiricelaya, J. Lafuente-Bartolome, I. G. Gur- 5

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