Interaction-Induced Shubnikov--de Haas Oscillations in Optical Conductivity of Monolayer ${\mathrm{MoSe}}_{2}$

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Interaction-Induced Shubnikov–de Haas Oscillations in Optical Conductivity of Monolayer ${MoSe}_{2}$

T. Smoleński, O. Cotlet, A. Popert, P. Back, Y. Shimazaki, P. Knüppel, N. Dietler, T. Taniguchi, K. Watanabe, M. Kroner, and A. Imamoglu

Phys. Rev. Lett. 123, 097403 – Published 30 August 2019

Abstract

We report polarization-resolved resonant reflection spectroscopy of a charge-tunable atomically thin valley semiconductor hosting tightly bound excitons coupled to a dilute system of fully spin- and valley-polarized holes in the presence of a strong magnetic field. We find that exciton-hole interactions manifest themselves in hole-density dependent, Shubnikov–de Haas–like oscillations in the energy and line broadening of the excitonic resonances. These oscillations are evidenced to be precisely correlated with the occupation of Landau levels, thus demonstrating that strong interactions between the excitons and Landau-quantized itinerant carriers enable optical investigation of quantum-Hall physics in transition metal dichalcogenides.

Received 19 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.097403

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Excitons Landau levels Shubnikov-de Haas effect Valleytronics

Transition metal dichalcogenides Two-dimensional electron system

Reflectivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Smoleński^1,2,*, O. Cotlet¹, A. Popert¹, P. Back¹, Y. Shimazaki¹, P. Knüppel¹, N. Dietler¹, T. Taniguchi³, K. Watanabe³, M. Kroner¹, and A. Imamoglu¹

¹Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
²Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
³National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan

^*Corresponding author. tomaszs@phys.ethz.ch

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Vol. 123, Iss. 9 — 30 August 2019

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Figure 1
(a) Optical microscope image of the gate-controlled ${MoSe}_{2}$ monolayer studied in this Letter. The monolayer was encapsulated between two layers of $h − BN$ , electrically contacted with a few-layer graphene (FLG) flake, and capped with the second FLG flake serving as a top gate (the boundaries of the flakes are marked with dashed lines). The carrier density was tuned by applying a gate voltage between Au/Ti electrodes connected to the FLG flakes. (b) Color-scale map presenting reflectance contrast spectra measured as a function of the gate voltage at $B = 0$ . The horizontal dashed lines mark the transitions between neutral and $n$ - or $p$ -doped regimes.
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Figure 2
(a), (b) Reflectance contrast spectra measured at $B = 16 T$ as a function of the gate voltage in $σ^{+}$ (a) or $σ^{-}$ (b) circular polarization. (c) Schematic illustrating the lowest-energy electronic subbands at the $K^{+}$ and $K^{-}$ valleys for a ${MoSe}_{2}$ monolayer subjected to an external magnetic field. The horizontal dashed lines show the positions of the Fermi level at the crossovers between different doping regimes, which are marked in (a) and (b).
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Figure 3
(a),(b) Gate-voltage dependencies of the linewidths (a) and energies (b) of the exciton (red) and attractive polaron (blue) resonances on the hole-doped side at $B = 16 T$ . The data was extracted by fitting the spectral profiles of both resonances in the polarization-resolved reflectance contrast spectra from Figs. 2 and 2. (c) Absolute values of the derivatives of the energies of both resonances with respect to the gate voltage. (d) Gate voltages $V_{g}$ corresponding to integer filling factors $ν$ determined based on the positions of the local minima of the exciton linewidth (independently marked by vertical dashed lines). Solid line represents the linear fit to the data for $V_{g} ≲ - 8 V$ , when the Schottky effects at the contact to ${MoSe}_{2}$ can be neglected, and hence when the hole density depends linearly on $V_{g}$ (for details, see the Supplemental Material [36]). (e),(f) Cartoons illustrating the exciton (e) and attractive polaron (f) configurations in the presence of Landau-quantized system of spin-polarized holes occupying only the states in $K^{+}$ valley under the influence of external magnetic field $B > 0$ .
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Figure 4
(a)–(c) Exciton linewidth (a), relative energy (b), and derivative of the energy with respect to $ν$ (c) calculated at $B = 16 T$ as a function of the filling factor using the developed theoretical model. The red (black) curves represent the results of the model including (excluding) the interaction effects.
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Figure 5
Gate voltages $V_{g} (ν, B)$ corresponding to integer filling factors $ν$ determined based on the positions of the exciton linewidth minima for different magnetic fields $B$ . The data are presented only in a linear-response regime of the gate (i.e., for $V_{g} ≲ - 8 V$ ), in which the hole density depends linearly on $V_{g}$ , and its value (marked on the right axis) can be obtained within the frame of the parallel-plate capacitor model (for details, see the Supplemental Material [36]). Solid lines represent the fit to the experimental data with a set of linear dependencies $V_{g} (ν, B) = V_{0} - δ ν B$ with two fitting parameters: $V_{0}$ representing the common origin of these curves, and $δ$ controlling their slopes.
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Physical Review Letters

Interaction-Induced Shubnikov–de Haas Oscillations in Optical Conductivity of Monolayer MoSe2

T. Smoleński, O. Cotlet, A. Popert, P. Back, Y. Shimazaki, P. Knüppel, N. Dietler, T. Taniguchi, K. Watanabe, M. Kroner, and A. Imamoglu

Phys. Rev. Lett. 123, 097403 – Published 30 August 2019

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Interaction-Induced Shubnikov–de Haas Oscillations in Optical Conductivity of Monolayer ${MoSe}_{2}$