Electrical Tuning of Exciton Binding Energies in Monolayer ${\mathrm{WS}}_{2}$

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Electrical Tuning of Exciton Binding Energies in Monolayer ${WS}_{2}$

Alexey Chernikov, Arend M. van der Zande, Heather M. Hill, Albert F. Rigosi, Ajanth Velauthapillai, James Hone, and Tony F. Heinz

Phys. Rev. Lett. 115, 126802 – Published 16 September 2015

Abstract

We demonstrate continuous tuning of the exciton binding energy in monolayer ${WS}_{2}$ by means of an externally applied voltage in a field-effect transistor device. Using optical spectroscopy, we monitor the ground and excited excitonic states as a function of gate voltage and track the evolution of the quasiparticle band gap. The observed decrease of the exciton binding energy over the range of about 100 meV, accompanied by the renormalization of the quasiparticle band gap, is associated with screening of the Coulomb interaction by the electrically injected free charge carriers at densities up to $8 \times 10^{12} {cm}^{- 2}$ . Complete ionization of the excitons due to the electrical doping is estimated to occur at a carrier density of several $10^{13} {cm}^{- 2}$ .

Received 10 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.126802

Authors & Affiliations

Alexey Chernikov¹, Arend M. van der Zande^1,2,3, Heather M. Hill¹, Albert F. Rigosi¹, Ajanth Velauthapillai^1,4, James Hone², and Tony F. Heinz^1,5,6

¹Departments of Physics and Electrical Engineering, Columbia University, New York, New York 10027, USA
²Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA
³Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
⁴Department of Physics and Materials Sciences Center, Philipps-Universität Marburg, Marburg 35032, Germany
⁵Department of Applied Physics, Stanford University, Stanford, California 94305, USA
⁶SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

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Vol. 115, Iss. 12 — 18 September 2015

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Figure 1
(a) Color plot of the reflectance contrast spectra for different gate voltages at a temperature of $T = 50 K$ . Charge neutrality point is estimated to be around $V_{g} = - 45 V$ , and the electron density increases roughly by $0.8 \times 10^{12} {cm}^{- 2}$ per 10 V. The evolution of the charged and neutral exciton peaks is shown by dotted lines. (b) Reflectance contrast spectra for selected gate voltages, offset for clarity. (c) Schematic illustration of the relevant part of the ${WS}_{2}$ band structure around the fundamental band gap transition with (top) and without (bottom) electron doping. The spin splitting of the conduction bands and the bright exciton transition are indicated by $Δ CBS$ and $X_{0}$ , respectively. The spin-split valence band lies much lower in energy and has been omitted for clarity.
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Figure 2
Second derivatives of the reflectance contrast spectra for gate voltages relative to the charge neutrality point of $Δ V_{g} = 0 V$ (a),(b) and $Δ V_{g} = 95 V$ (c),(d), corresponding to an estimated electron doping density of about $8 \times 10^{12} {cm}^{- 2}$ . The measured spectra are indicated by the black lines and the results of the multi-Lorentzian model by red and blue curves. Both experimental and simulated curves are smoothed over a spectral range of 10 meV after each derivative is taken. The simulated curve without the $n = 2$ and $n = 3$ resonances is included in (b) for comparison.
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Figure 3
Peak energies for the $n = 3$ (a), $n = 2$ (b), and $n = 1$ (c) exciton states as a function of gate voltage $Δ V_{g}$ relative to the charge neutrality point. The estimated electron doping density scales roughly by $0.8 \times 10^{12} {cm}^{- 2}$ per 10 V. Data from four individual measurements (light colored squares) at each gate voltage are presented together with the respective averages (dark colored squares) and linear line fits (solid curves). The vertical scale of the energy axis is the same in all three plots.
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Figure 4
(a) Schematic illustration of the absorption spectra for an undoped (top) and doped (bottom) 2D semiconductor. The quasiparticle band-gap energy $E_{gap}$ is represented by the dashed line, and the ground and excited exciton states are indicated by $n = 1$ and $n > 1$ , respectively. (b) Evolution of the exciton binding energies as a function of the relative gate voltage $Δ V_{g}$ as estimated from the minimum and maximum shifts of the band gap. The estimated electron density increases by roughly $0.8 \times 10^{12} {cm}^{- 2}$ per 10 V. Values for the exciton binding energies at $Δ V_{g} = 35 V$ are fixed from Ref. [8] and are represented by circles. (c) Absolute energies of the $n = 1, 2, 3$ exciton states and the estimated minimum and maximum shifts of the band gap. Linear fits to the experimental data are used in (b) and (c) for clarity.
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Physical Review Letters

Electrical Tuning of Exciton Binding Energies in Monolayer WS2

Alexey Chernikov, Arend M. van der Zande, Heather M. Hill, Albert F. Rigosi, Ajanth Velauthapillai, James Hone, and Tony F. Heinz

Phys. Rev. Lett. 115, 126802 – Published 16 September 2015

Abstract

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Electrical Tuning of Exciton Binding Energies in Monolayer ${WS}_{2}$