Probing many-body quantum states in single InAs quantum dots: Terahertz and tunneling spectroscopy

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Probing many-body quantum states in single InAs quantum dots: Terahertz and tunneling spectroscopy

Y. Zhang, K. Shibata, N. Nagai, C. Ndebeka-Bandou, G. Bastard, and K. Hirakawa

Phys. Rev. B 91, 241301(R) – Published 3 June 2015

Abstract

We have investigated the many-body quantum states in single InAs quantum dots (QDs) by simultaneously obtaining the terahertz (THz) intersublevel transition and single electron tunneling spectra. It is found that the intersublevel transition energies measured in the few-electron region are systematically larger than the excited state (ES) energies determined from the transport measurements. We show that tunneling and THz spectroscopy probe the same many-body excited states in the QDs, but their sensitivities depend on their selection rules. In the many-electron region, we observe THz peaks whose energies coincide with the tunneling ESs.

Received 26 February 2015
Revised 12 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.241301

Authors & Affiliations

Y. Zhang^1,*, K. Shibata^1,2,†, N. Nagai¹, C. Ndebeka-Bandou^1,3, G. Bastard^1,3, and K. Hirakawa^1,2,‡

¹Center for Photonics Electronics Convergence, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
²Institute for Nano Quantum Information Electronics, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
³Laboratoire Pierre Aigrain, Ecole Normale Superieure, 24 rue Lhomond, F-75005 Paris, France

^*Electronic mail: zhangya@iis.u-tokyo.ac.jp
^†Permanent address: Department of Electronics and Intelligent Systems, Tohoku Institute of Technology, Sendai 982-8577, Japan.
^‡Electronic mail: hirakawa@iis.u-tokyo.ac.jp

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Issue

Vol. 91, Iss. 24 — 15 June 2015

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Images

Figure 1
(a) Cross section of the QD-SET sample. (b) SEM images of QD-SET A with a bowtie antenna structure. The QD is marked by a red circle. (c) Coulomb stability diagram of QD-SET A. White solid lines are guides to the eye for the boundaries of Coulomb diamonds. White dashed lines denote the ESs. The numbers in the Coulomb diamonds denote the number of electrons in the dot. Pink curves are the photocurrent spectra. (d) THz-induced photocurrent as a function of $V_{G}$ measured on QD-SET A by applying a small source-drain voltage $(V_{DS} = 0.25 mV)$ . (e) Photocurrent spectra measured at various $V_{G}$ on QD-SET A. (f) Coulomb stability diagram of QD-SET B. Pink curves are the photocurrent spectra. (g) THz-induced photocurrent as a function of $V_{G}$ measured on QD-SET B. (h) Photocurrent spectra measured at various $V_{G}$ on the QD-SET B.
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Figure 2
(a) Excited state (ES) energies determined from the transport measurements (triangles) and the THz measurements (circles) are plotted as a function of the electron number N. The data were summarized for three QD-SETs. (b) Schematic illustration of a Coulomb stability diagram that shows ES lines (dashed lines). The height of point P expresses the ES energy. (c) Energy band diagram for the ES spectroscopy in the tunneling measurement. (d) Energy band diagram for the THz intersublevel transition spectroscopy. (e) Schematic Coulomb stability diagram for electron numbers $N = 1$ and 2. Two ESs (triplet and singlet) are shown by a dashed line and a dotted line, respectively. The triplet ES (T) tends to be more visible than the singlet ES (S) in the stability diagram, whereas the THz spectra measure only the singlet ES.
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Figure 3
(a) A SEM image of a QDH-SET sample. The QDH is marked by a red rectangle. (b) A Coulomb stability diagram of the QDH-SET. The numbers in the figure $(L, L + 1, L + 2, ...)$ denote the numbers of electrons in the QDH. (c) THz-induced photocurrent as a function of $V_{G}$ measured at $V_{DS} = 0.25 mV$ . (d) Photocurrent spectra measured at various $V_{G}$ on the QDH-SET with $V_{DS} = 0.25 mV$ .
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Figure 4
(a) The THz spectra and the Coulomb stability diagram for QDH-SET. Pink curves are the photocurrent spectra and the numbers shown above the spectra denote the electron numbers in the QD. The black dashed lines show the ESs that have the same excitation energies with the THz photocurrent peaks. (b) and (c) show the THz spectra and the Coulomb stability diagrams for $N = L + 1$ and $L + 6$ , respectively. The dotted lines indicate the photocurrent peaks that have the same energy as the transport ESs.
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