Electron and Hole $g$ Tensors of Neutral and Charged Excitons in Single Quantum Dots by High-Resolution Photocurrent Spectroscopy

Shiyao Wu, Kai Peng, Xin Xie, Jingnan Yang, Shan Xiao, Feilong Song, Jianchen Dang, Sibai Sun, Longlong Yang, Yunuan Wang, Shushu Shi, Jiongji He, Zhanchun Zuo, and Xiulai Xu

Phys. Rev. Applied 14, 014049 – Published 16 July 2020

Abstract

We report high-resolution photocurrent (PC) spectroscopy of a single self-assembled $InAs$ / $GaAs$ quantum dot embedded in an $n$ - $i$ Schottky device in an applied vector magnetic field. The PC spectra of positively charged excitons ( $X^{+}$ ) and neutral excitons ( $X^{0}$ ) are obtained by two-color resonant excitation. With an applied magnetic field in the Voigt geometry, the double- $Λ$ energy-level structure of $X^{+}$ and the dark states of $X^{0}$ are observed clearly in the PC spectra. In the Faraday geometry, the PC amplitude of $X^{+}$ decreases and is then quenched with increasing magnetic field, which provides a new way to determine the relative sign of the electron and hole $g$ -factors. With an applied vector magnetic field, the electron and hole $g$ -factor tensors of $X^{+}$ and $X^{0}$ are obtained. The anisotropy of the hole $g$ -factors of both $X^{+}$ and $X^{0}$ is larger than that of the electron $g$ -factors.

Received 11 March 2020
Revised 13 May 2020
Accepted 8 June 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.014049

Physics Subject Headings (PhySH)

Excitons Optoelectronics Photoconductivity Quantum information with solid state qubits

III-V semiconductors Quantum dots Schottky barriers

Optical microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shiyao Wu^1,2, Kai Peng^1,2, Xin Xie^1,2, Jingnan Yang^1,2, Shan Xiao^1,2, Feilong Song^1,2, Jianchen Dang^1,2, Sibai Sun^1,2, Longlong Yang^1,2, Yunuan Wang^1,3, Shushu Shi^1,2, Jiongji He^1,2, Zhanchun Zuo^1,2, and Xiulai Xu ^1,2,4,*

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
³Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
⁴Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*xlxu@iphy.ac.cn

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Vol. 14, Iss. 1 — July 2020

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Figure 1
(a) Schematic diagram of the $n$ - $i$ Schottky device and PC measurement in a vector magnetic field. Here, $θ$ is the angle between the magnetic field ( $B$ ) and the growth axis of the QDs ( $z$ direction). (b) Two-color excitation scheme used for the $X^{+}$ PC measurements. The solid and wavy arrows represent the excitation and tunneling processes, respectively, of carriers. (c) PC spectra of $X^{0}$ and $X^{+}$ under two-color excitation. The black solid points represent the pure $X^{0}$ PC spectrum with $E_{L}^{0} = 1347.684$ meV. The red, purple, and blue solid points represent the measured PC spectra of $X^{+}$ for different energies of the second laser, $E_{L}^{+}$ . (d) Subtracted PC spectra of $X^{+}$ for different energies of the second laser. The top $x$ axis represents the Stark shift of $X^{+}$ . (e) Stark shifts of $X^{0}$ and $X^{+}$ as a function of the electric field and the bias voltage obtained from the single-QD PL (empty squares) and PC (solid squares) spectra. The solid red lines represent quadratic fits to the quantum confined Stark effect for $X^{0}$ and $X^{+}$ . The fitting parameters for $E (0)$ , $p$ , and $β$ are given in the table in the inset.
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Figure 2
(a) Energy-level structure of $X^{+}$ in a magnetic field. Here, the two inner transitions (blue solid arrows), with an angular momentum of $M = \pm 2$ , are dark-state transitions. The two outer transitions (red solid arrows), with $M = \pm 1$ , are bright-state transitions. (b) Zeeman splitting of $| X^{+} ⟩$ and $| h ⟩$ states in the Voigt geometry. (c) PC spectra of $X^{+}$ in a magnetic field from 0 to 4 T in the Voigt geometry. The spectra are shifted for clarity. (d) Polarization-resolved PL spectra of $X^{+}$ in a magnetic field from 0 to 4 T in the Voigt geometry. The spectra are shifted for clarity. (e) Polarization-resolved PC spectra of $X^{+}$ in a 4-T Voigt magnetic field, where the short blue and red lines on the right are guides to the eye for the dark and bright states, respectively.
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Figure 3
(a) Schematic diagram of the carrier transitions and decays in $X^{+}$ in a magnetic field with $| g_{e} | \neq | g_{h} |$ (left panel) and $| g_{e} | = | g_{h} |$ (right panel). The solid and wavy lines represent the excitation and tunneling processes, respectively. (b) PC spectra of $X^{+}$ in a magnetic field in the Faraday geometry from 0 to 2.5 T. The top $x$ axis represents the energy shift compared with the $X^{+}$ transition energy at zero magnetic field. The spectra are shifted for clarity. (c) Schematic diagram of $X^{+}$ and $X^{0}$ PC spectra in zero magnetic field (bottom panel) and a Faraday magnetic field (top panel) under the condition $g_{e} g_{h} < 0$ . Here, the red and blue curves represent the PC spectra of $X^{0}$ and $X^{+}$ , respectively. (d) Magneto-PC mapping of $X^{+}$ in a 4-T vector magnetic field at angles from $90^{\circ}$ to $65^{\circ}$ . Here, the red and blue dashed lines are guides to the eye for the bright- and dark-state transitions, respectively, of $X^{+}$ . (e) PC spectra of $X^{+}$ and $X^{0}$ in a 4-T vector magnetic field with $θ$ from $90^{\circ}$ to $60^{\circ}$ . The red solid curves are the PC spectra of $X^{+}$ , and the blue dashed curves are the PC spectra of $X^{0}$ . (f) Electron and hole $g$ -factors of $X^{+}$ as a function of the angle $θ$ . The solid dots are the extracted electron and hole $g$ -factors, with error bars of about 0.02. The red and black dots at $θ = 0^{\circ}$ show $| g_{e, z} |$ and $| g_{h, z} |$ derived by fitting the extracted data to Eq. (1) (solid curves) under the condition $| g_{e, z} | + | g_{h, z} | = 3.10 \pm 0.02$ .
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Figure 4
(a) Energy-level structure of $X^{0}$ in a magnetic field in the Voigt geometry. Here, $δ_{0}$ represents the energy difference between the bright and the dark states, and $δ_{1}$ and $δ_{2}$ represent the FSS of the bright and dark states, respectively; these are referred to as the exchange parameters. (b) Zeeman splitting of bright and dark states in a magnetic field in the Voigt geometry. The diamagnetic shift is deduced. Here, the circles are the extracted data, and the solid curves are fitted results with consideration of the exchange parameters $δ_{0}$ , $δ_{1}$ , and $δ_{2}$ . (c) Polarization-resolved PC spectra of $X^{0}$ in magnetic fields from 0 to 4 T in the Voigt geometry. The spectra are shifted for clarity. (d) Linear-polarization-resolved PC spectra at 4 T in the Voigt geometry. The short blue and red lines are guides to the eye for the dark and bright states of $X^{0}$ .
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Figure 5
(a) PC spectra of $X^{0}$ in a magnetic field from 0 to 9 T in the Faraday geometry. The top $x$ axis represents the energy shift compared with the $X^{+}$ transition energy at zero magnetic field. The spectra are shifted for clarity. (b) Top panel: energy of $X^{0}$ extracted from part (a) as a function of the magnetic field, offset by the mean at 0 T. Bottom panel: Zeeman splitting of $X^{0}$ , from which the $g$ -factor is derived as $3.03 \pm 0.03$ . (c) Magneto-PC mapping of $X^{0}$ in a 4-T vector magnetic field. The red and blue dashed lines represent the bright and dark states, respectively. (d) Fitting results for the splitting of $X^{0}$ in a vector magnetic field. The circles represent the extracted data for the four transitions in part (c) without the diamagnetic shift. The solid curves show the fitted results. The fitted exchange parameters are shown in the inset table.
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