In-Plane Electric-Field-Induced Orbital Hybridization of Excitonic States in Monolayer ${\mathrm{WSe}}_{2}$

In-Plane Electric-Field-Induced Orbital Hybridization of Excitonic States in Monolayer ${WSe}_{2}$

Bairen Zhu, Ke Xiao, Siyuan Yang, Kenji Watanabe, Takashi Taniguchi, and Xiaodong Cui

Phys. Rev. Lett. 131, 036901 – Published 17 July 2023

Abstract

The giant exciton binding energy and the richness of degrees of freedom make monolayer transition metal dichalcogenide an unprecedented playground for exploring exciton physics in 2D systems. Thanks to the well-energetically separated excitonic states, the response of the discrete excitonic states to the electric field could be precisely examined. Here we utilize the photocurrent spectroscopy to probe excitonic states under a static in-plane electric field. We demonstrate that the in-plane electric field leads to a significant orbital hybridization of Rydberg excitonic states with different angular momentum (especially orbital hybridization of $2 s$ and $2 p$ ) and, consequently, optically actives $2 p$ -state exciton. Besides, the electric-field controlled mixing of the high lying exciton state and continuum band enhances the oscillator strength of the discrete excited exciton states. This electric field modulation of the excitonic states in monolayer TMDs provides a paradigm of the manipulation of 2D excitons for potential applications of the electro-optical modulation in 2D semiconductors.

Received 7 October 2021
Revised 6 May 2023
Accepted 6 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.036901

Physics Subject Headings (PhySH)

Electric field effects Excitons

2-dimensional systems

Optical techniques Photocurrent spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bairen Zhu^1,*,†, Ke Xiao^2,*, Siyuan Yang², Kenji Watanabe ³, Takashi Taniguchi⁴, and Xiaodong Cui^2,‡

¹Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
²Physics Department, University of Hong Kong, Hong Kong, China
³Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁴International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*These authors contributed equally to this work.
^†zhubair@zjut.edu.cn
^‡xdcui@hku.hk

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Vol. 131, Iss. 3 — 21 July 2023

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Figure 1
(a) Optical microscopic image of the $h BN$ -encapsulated monolayer ${WSe}_{2}$ with few-layer graphene (FLG) as electric contacts. The different layers are marked by dashed lines of different colors. The white scale bar is $5 μ m$ . (b) Schematic of the device on a transparent quartz substrate for the photocurrent measurement. (c)–(d) The reflection and photocurrent mappings of the device at $V_{d s} = + 5 V$ and $T = 10 K$ . The scanning range covers the marked area in (a). Two electric contacts of FLG and $1 L − {WSe}_{2}$ are also labeled for reference. (e)–(f) The reflection and photocurrent mappings at $V_{d s} = - 5 V$ . Photoluminescence of the $A − 1 s$ exciton (g) and $A − 2 s$ exciton (h) on the spot where the photocurrent is taken as a function of the source-drain voltage at $T = 10 K$ . The fake colors in these mappings present the signal magnitude with the linear spectra scales where the minimum starts from blue to red at maximum.
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Figure 2
(a) Reflectance contrast and photocurrent spectra at $V_{d s} = + 2 V$ of $h BN$ -encapsulated monolayer ${WSe}_{2}$ devices. (b) Photocurrent spectra on a log scale under various in-plane electric fields that are extracted by excitonic dc stark effect of $A − 1 s$ exciton. Enlargement of the shifts of $A 1 s$ and the data under the positive electric field are shown in Supplemental Material, Sec. 2 [22]. (c) The energy shift of the $1 s$ exciton is proportional to the square of electric field $F$ and exciton in-plane polarizability $α$ ( $\sim - 1 / 2 α F^{2}$ ) with the fitting error bar of energy. The in-plane electric fields are extracted with a $h$ -BN dielectric constant $ε_{B N} = 4.5$ . The error bars of electric fields result from the uncertainty in the $h$ -BN dielectric constant $ε_{B N}$ (3.0–4.5). The inhomogeneity of in-plane electric field owing to the sample or substrate inhomogeneity is shown in Supplemental Material, Sec. 3 [22]. The in-plane polarizability of the $B$ exciton is found to be smaller than that of the $A$ exciton, implying a larger exciton binding energy owing to the larger effective mass. Similar data from other devices are presented in Supplemental Material, Sec. 4 [22]. (d) The calculated electroabsorption of 1L ${WSe}_{2}$ on a log scale from 0 to $16 V / μ m$ , consistent with the experimental results in (b). The dashed lines denote the electroabsorption spectra without the $2 p$ state.
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Figure 3
(a) The spatial distribution of excitonic envelope wave function with different orbitals and envelope functions as a function of the in-plane electric field. In region I marked in blue, all exciton states preserve without significant change. The $1 s$ state keeps unchanged until $F = 20 V / μ m$ . In region IIa marked in pink, $2 p_{x}$ , $2 p_{y}$ , and $2 s$ states distort evidently owing to the orbital hybridization with some neighboring states. (b)–(e) The analysis of the orbital composition of hybrid excitons as a function of in-plane electric field. The error bar denotes the state energy broadening.
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Figure 4
Energies of hybrid excitons from experimental photocurrent spectra (dots) and calculated electroabsorption (solid lines), respectively.
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Physical Review Letters

In-Plane Electric-Field-Induced Orbital Hybridization of Excitonic States in Monolayer WSe2

Bairen Zhu, Ke Xiao, Siyuan Yang, Kenji Watanabe, Takashi Taniguchi, and Xiaodong Cui

Phys. Rev. Lett. 131, 036901 – Published 17 July 2023

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In-Plane Electric-Field-Induced Orbital Hybridization of Excitonic States in Monolayer ${WSe}_{2}$