Direct observation of giant binding energy modulation of exciton complexes in monolayer $\mathrm{MoS}{\mathrm{e}}_{2}$

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Direct observation of giant binding energy modulation of exciton complexes in monolayer $MoS e_{2}$

Garima Gupta, Sangeeth Kallatt, and Kausik Majumdar

Phys. Rev. B 96, 081403(R) – Published 7 August 2017

Abstract

Screening due to the surrounding dielectric medium reshapes the electron-hole interaction potential and plays a pivotal role in deciding the binding energies of strongly bound exciton complexes in quantum confined monolayers of transition metal dichalcogenides (TMDs). However, owing to strong quasiparticle band-gap renormalization in such systems, a direct quantification of estimated shifts in binding energy in different dielectric media remains elusive using optical studies. In this work, by changing the dielectric environment, we show a conspicuous photoluminescence peak shift at low temperature for higher energy excitons $(2 s, 3 s, 4 s, 5 s)$ in monolayer $MoS e_{2}$ , while the $1 s$ exciton peak position remains unaltered – a direct evidence of varying compensation between screening induced exciton binding energy modulation and quasiparticle band-gap renormalization. The estimated modulation of binding energy for the $1 s$ exciton is found to be $58.6 %$ $(72.8 %$ for $2 s, 75.85 %$ for $3 s$ , and $85.6 %$ for $4 s)$ by coating an $A l_{2} O_{3}$ layer on top, while the corresponding reduction in quasiparticle band-gap is estimated to be 246 meV. Such direct evidence of large tunability of the binding energy of exciton complexes as well as the band-gap in monolayer TMDs holds promise of novel device applications.

Received 20 March 2017
Revised 30 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.081403

Physics Subject Headings (PhySH)

Band gap Excitons

Transition metal dichalcogenides

Fluorescence spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Garima Gupta¹, Sangeeth Kallatt^1,2, and Kausik Majumdar^1,*

¹Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560012, India
²Center for Nano Science and Engineering, Indian Institute of Science, Bangalore 560012, India

^*Corresponding author: kausikm@iisc.ac.in

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Vol. 96, Iss. 8 — 15 August 2017

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Figure 1
(a) Schematic representation of the effect of image charge arising from the introduction of a dielectric layer in the vicinity of monolayer $MoS e_{2}$ , with an enhancement of exciton Bohr radius. (b) PL spectra of single layer $MoS e_{2}$ , acquired at 8 K, for samples M1 and M2. $A_{1 s}^{0}$ and $A_{1 s}^{-}$ represent the neutral 1s A exciton and the corresponding negatively charged trion. (c) PL spectra of monolayer $MoS e_{2}$ obtained at room temperature for different top and bottom dielectric materials. The $A_{1 s}^{0}$ exciton peak energy is nearly unaffected with screening, showing a maximum of 10 meV shift. (d) An increase in screening modifies the quasiparticle band gap $(Δ E_{g})$ , bringing the continuum down to $continuu m^{^{'}}$ , and reduces the binding energy of exciton states. These two effects compete and decide the final transition energy of various exciton states upon modified surroundings. The compensation is nearly equal for the $1 s$ exciton state, resulting in unchanged $A_{1 s}^{0}$ energy $(Δ E_{g} = Δ E_{b}^{1 s})$ . The binding energy reduction decreases in magnitude for higher energy exciton states $(| Δ E_{b}^{1 s} | > | Δ E_{b}^{2 s} | > | Δ E_{b}^{3 s} |)$ , resulting in only partial compensation of the renormalized band-gap induced shift. This suggests observation of redshift in the $A_{2 s}^{0}$ and $A_{3 s}^{0}$ peaks when surrounded by a medium with large dielectric constant.
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Figure 2
(a)−(d) The experimental PL data for sample M1 (in gray) in the energy range $1.75 - 2.0$ eV, measured at sample temperatures ranging from 8 to 35 K. Four peaks are obtained from fitting the data, namely, $A_{2 s}^{0}$ exciton (orange), $A_{3 s}^{0}$ exciton (pink), $B_{1 s}^{-}$ trion (purple), and $B_{1 s}^{0}$ exciton (green). The $B_{1 s}^{-}$ trion peak, about 30 meV below $B_{1 s}^{0}$ , shows a slight increase in intensity with temperature. (e) Schematic of lowest energy bright (left panel) and dark (right panel) $A$ trion states. The dotted and solid lines in the conduction band (valence band) correspond to spin-up (down) and spin-down (up) states of electrons (hole) in monolayer $MoS e_{2}$ . The bright state $A_{1 s, B}^{-}$ is at lower energy than the $A_{1 s, D}^{-}$ dark state. (f) The lowest energy bright (left panel) and dark (right panel) $B$ trion states suggest that the bright $B_{1 s, B}^{-}$ state is at higher energy than the dark $B_{1 s, D}^{-}$ trion state. This explains the slight increase in $B_{1 s, B}^{-}$ intensity with temperature in (a)–(d).
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Figure 3
(a) PL peak positions for higher energy $A$ exciton states $(A_{2 s}^{0}$ to $A_{5 s}^{0})$ in sample M2 (bottom panel). For reference, spectrum from sample M1 is shown in the top panel. Clear redshifts for the $A_{2 s}^{0}$ and $A_{3 s}^{0}$ peaks are observed in M2 compared with M1. The $B_{1 s}^{-}$ trion peak close to the $B_{1 s}^{0}$ peak for both samples is also discernible. (b) The $A_{1 s}^{0}$ exciton peak is almost similar for samples M1 and M2 at various measurement temperatures. (c) The $A_{2 s}^{0}, A_{3 s}^{0}$ PL peak positions for M1 and M2 at different temperatures testify to the strong PL peak shift for higher energy exciton states.
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Figure 4
(a) Schematic of the five-dielectric-layer configuration considered for quantitative binding energy estimations of excitons in monolayer $MoS e_{2}$ including a 3 Å van der Waals gap. (b) The hole distribution in the $x − z$ cross-section plane of $MoS e_{2}$ . (c) Converged potential due to the distributed hole in the plane of the monolayer $MoS e_{2}$ for samples M1 and M2.
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Figure 5
Experimental PL peak positions (solid circles) and the corresponding values predicted from the distributed charge model (open symbol). The continuum levels are represented by dashed lines (red for sample M1 and blue for sample M2). The binding energy of different exciton states is extracted from the difference between the continuum and the PL peak position, as schematically illustrated for the $1 s$ and $2 s$ states.
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Physical Review B

covering condensed matter and materials physics

Direct observation of giant binding energy modulation of exciton complexes in monolayer $MoS e_{2}$

Garima Gupta, Sangeeth Kallatt, and Kausik Majumdar

Phys. Rev. B 96, 081403(R) – Published 7 August 2017

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Physical Review B

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Direct observation of giant binding energy modulation of exciton complexes in monolayer MoSe2

Garima Gupta, Sangeeth Kallatt, and Kausik Majumdar

Phys. Rev. B 96, 081403(R) – Published 7 August 2017

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Direct observation of giant binding energy modulation of exciton complexes in monolayer $MoS e_{2}$