Direct Determination of Band-Gap Renormalization in the Photoexcited Monolayer ${\mathrm{MoS}}_{2}$

Direct Determination of Band-Gap Renormalization in the Photoexcited Monolayer ${MoS}_{2}$

Fang Liu, Mark E. Ziffer, Kameron R. Hansen, Jue Wang, and Xiaoyang Zhu

Phys. Rev. Lett. 122, 246803 – Published 21 June 2019

Abstract

A key feature of monolayer semiconductors, such as transition-metal dichalcogenides, is the poorly screened Coulomb potential, which leads to a large exciton binding energy ( $E_{b}$ ) and strong renormalization of the quasiparticle band gap ( $E_{g}$ ) by carriers. The latter has been difficult to determine due to a cancellation in changes of $E_{b}$ and $E_{g}$ , resulting in little change in optical transition energy at different carrier densities. Here, we quantify band-gap renormalization in macroscopic single crystal ${MoS}_{2}$ monolayers on ${SiO}_{2}$ using time and angle-resolved photoemission spectroscopy. At an excitation density above the Mott threshold, $E_{g}$ decreases by as much as 360 meV. We compare the carrier density-dependent $E_{g}$ with previous theoretical calculations and show the necessity of knowing both doping and excitation densities in quantifying the band gap.

Received 19 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.246803

Physics Subject Headings (PhySH)

Carrier generation & recombination Excitons

Transition metal dichalcogenides Two-dimensional electron system

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Fang Liu, Mark E. Ziffer, Kameron R. Hansen, Jue Wang, and Xiaoyang Zhu^*

Department of Chemistry, Columbia University, New York, New York 10027, USA

^*To whom correspondence should be addressed. xyzhu@columbia.edu

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Vol. 122, Iss. 24 — 21 June 2019

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Figure 1
The macroscopic single crystal ${MoS}_{2}$ monolayer sample and characterization. (a) Schematics of TR-ARPES experiment, combining the femtosecond visible pump (green) and EUV probe (purple). The photoelectrons are collected by the hemispherical analyzer at a specific angle $θ$ from the surface normal, corresponding to emission from a $K$ valley. (b) Image of the single crystal ${MoS}_{2}$ monolayer. We deposit Au films in the dashed areas for electrical contact and grounding. (c) Complex dielectric function ( $ϵ = ϵ_{1} + i ϵ_{2}$ ) of the monolayer ${MoS}_{2}$ determined from reflectance spectroscopy and (d) photoluminescence spectrum of the ${MoS}_{2}$ monolayer at room temperature.
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Figure 2
TR-ARPES from monolayer ${MoS}_{2}$ . (a),(b) EUV ARPES of single crystal ${MoS}_{2}$ monolayer without and with the visible pump excitation ( $Δ t = 0$ ). The APRES spectra is collected at $K$ valley along $Γ$ to $K$ direction. The visible pump is at a photon energy of 2.2 eV. (c) Corresponding electron energy distribution curves (EDC). The solid lines are Gaussian functional fits. The horizontal marks represent the edges of the EDCs, corresponding to $E_{0} + 2 σ$ . The spin orbit splitting at $K$ valley is not resolved under the current energy resolution. The excitation density from the pump pulse is $n_{e / h} = (2.3 \pm 0.5) \times 10^{13} {cm}^{- 2}$ . The conduction band signal is magnified by $10 \times$ for clarity.
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Figure 3
Dynamics of band renormalization. All panels are shown as a function of pump-probe delay: (a) and (b) are 2D pseudocolor (intensity) plots of EDC spectra collected individually for conduction band and valence band, respectively; (c) CBM and VBM positions extracted from EDC scans shown in panels (a) and (b); (d) band gap $E_{g}$ (gray) with biexponential fit (black solid line); (e) conduction (blue) and valence (red) band photoelectron intensities; and (f) full width at half maximum of valence band. To obtain the EDCs in (a) and (b), the photoelectron signal is integrated from 1.1 to $1.4 Å^{- 1}$ . The CBM is fixed at the time-averaged value of 0.223 eV in the calculation of the band gap in (d). The initial excitation density is $n_{e / h} = 1.3 \times 10^{13} {cm}^{- 2}$ and the sample is at 295 K. The color scales in (a) and (b) are normalized (0–1).
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Figure 4
Comparison of experimental band gaps with theoretical calculations. Solid circles are experimental band gaps for monolayer ${MoS}_{2}$ determined by TR-ARPES as a function of total doping density ( $n_{0} + 2 n_{e / h}$ ). The solid curves are theoretical results for electron doping (red [6] and blue [44]) or $e / h$ pair generation from optical excitation (green) [7].
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Physical Review Letters

Direct Determination of Band-Gap Renormalization in the Photoexcited Monolayer MoS2

Fang Liu, Mark E. Ziffer, Kameron R. Hansen, Jue Wang, and Xiaoyang Zhu

Phys. Rev. Lett. 122, 246803 – Published 21 June 2019

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Direct Determination of Band-Gap Renormalization in the Photoexcited Monolayer ${MoS}_{2}$