Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer ${\mathrm{MoS}}_{2}$

Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer ${MoS}_{2}$

Kaiyuan Yao, Aiming Yan, Salman Kahn, Aslihan Suslu, Yufeng Liang, Edward S. Barnard, Sefaattin Tongay, Alex Zettl, Nicholas J. Borys, and P. James Schuck

Phys. Rev. Lett. 119, 087401 – Published 25 August 2017

Abstract

Optoelectronic excitations in monolayer ${MoS}_{2}$ manifest from a hierarchy of electrically tunable, Coulombic free-carrier and excitonic many-body phenomena. Investigating the fundamental interactions underpinning these phenomena—critical to both many-body physics exploration and device applications—presents challenges, however, due to a complex balance of competing optoelectronic effects and interdependent properties. Here, optical detection of bound- and free-carrier photoexcitations is used to directly quantify carrier-induced changes of the quasiparticle band gap and exciton binding energies. The results explicitly disentangle the competing effects and highlight longstanding theoretical predictions of large carrier-induced band gap and exciton renormalization in two-dimensional semiconductors.

Received 9 March 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.087401

Physics Subject Headings (PhySH)

Band gap Defects Electronic structure Excitons Photonics Spin-orbit coupling Surface states Valleytronics

Quantum wells Semiconductor compounds

Optical absorption spectroscopy Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kaiyuan Yao^1,2, Aiming Yan^3,4, Salman Kahn³, Aslihan Suslu⁵, Yufeng Liang¹, Edward S. Barnard¹, Sefaattin Tongay⁵, Alex Zettl^3,4,6, Nicholas J. Borys^1,7,*, and P. James Schuck^1,8,†

¹Molecular Foundry Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
²Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
³Department of Physics, University of California, Berkeley, California 94720, USA
⁴Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁵Department of Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
⁶Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁷Department of Physics, Montana State University, Bozeman, Montana 59717, USA
⁸Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA

^*njborys@lbl.gov
^†pjschuck@lbl.gov

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Vol. 119, Iss. 8 — 25 August 2017

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Figure 1
(a) Schematic of gate-dependent PLE spectroscopy on monolayer ${MoS}_{2}$ . (b) Normalized PL spectra measured under different gate voltages with 2.5 eV excitation. The inset shows the dependence of defect PL yield as a function of gate voltage.
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Figure 2
Identification of the quasiparticle band gap in monolayer ${MoS}_{2}$ from PLE spectroscopy. (a) Dependence of the yield of DX emission on excitation energy (blue dots), overlaid on the absorption spectrum (gray, taken from samples transferred to a quartz substrate). The inset shows the color contour of normalized PL spectra measured at different excitation energies. (b) Comparison of the defect PL spectra (normalized to the $A$ exciton; full spectra are shown in Supplemental Material [35]) under excitation energies that are on and off resonance of the continuum edge and $B$ exciton. (c) Schematic level diagrams showing the relevant relaxation pathways of photogenerated excitations. A complete diagram is shown in Supplemental Material [35]. (d) Experimental PLE spectrum (gray dots) and total fit (black solid line) with contribution from the continuum (blue dotted line, with offset) and tail of the $C$ exciton (magenta dotted line).
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Figure 3
Gate-dependent PLE spectroscopy of monolayer ${MoS}_{2}$ . (a) PLE spectra of the integrated emission measured at different gate voltages. Experimental data, total fit, and the continuum contribution (with offset) are represented as gray dots, blue solid lines, and blue dashed lines, respectively. The PLE intensities are normalized to the oscillator strength (i.e., step height) of the fitted continuum function. (b) The excitation-energy dependent relative yield of DX emission at different gate voltages. The arrows in (a) and (b) represent the same energy of $E_{con}$ fitted from (a) as described in the text.
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Figure 4
Carrier-induced renormalization of the quasiparticle band gap of monolayer ${MoS}_{2}$ . (a) Dependence on electron doping concentration $n_{e}$ of the measured continuum onset energy $E_{con}$ (red squares) and quasiparticle band gap $E_{g}$ (blue dots). Predicted quasiparticle band gap energies from previous studies [23, 42, 47, 48, 49] are also plotted for comparison (orange crosses). (b) Direct comparison of the measured change of quasiparticle band gap (blue dots) to previous theoretical predictions (orange crosses) [23].
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Figure 5
Carrier-induced renormalization of the exciton binding energy in monolayer ${MoS}_{2}$ . (a) Dependence of the absorption energies of the neutral $A$ exciton (blue dots) and charged $A^{-}$ trion (red diamonds) on gate voltage. (b) Renormalization of the binding energy of the neutral $A$ exciton with electron concentration.
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Physical Review Letters

Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer MoS2

Kaiyuan Yao, Aiming Yan, Salman Kahn, Aslihan Suslu, Yufeng Liang, Edward S. Barnard, Sefaattin Tongay, Alex Zettl, Nicholas J. Borys, and P. James Schuck

Phys. Rev. Lett. 119, 087401 – Published 25 August 2017

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Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer ${MoS}_{2}$