Attractive Coulomb interactions in a triple quantum dot

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Attractive Coulomb interactions in a triple quantum dot

Changki Hong, Gwangsu Yoo, Jinhong Park, Min-Kyun Cho, Yunchul Chung, H.-S. Sim, Dohun Kim, Hyungkook Choi, Vladimir Umansky, and Diana Mahalu

Phys. Rev. B 97, 241115(R) – Published 22 June 2018

Abstract

Electron pairing due to a repulsive Coulomb interaction in a triple quantum dot (TQD) is experimentally studied. It is found that electron pairing in two dots of a TQD is mediated by the third dot, when the third dot strongly couples with the other two via Coulomb repulsion so that the TQD is in the twofold degenerate ground states of (1,0,0) and (0,1,1) charge configurations. Using the transport spectroscopy that monitors electron transport through each individual dot of a TQD, we analyze how to achieve the degeneracy in experiments, how the degeneracy is related to electron pairing, and the resulting nontrivial behavior of electron transport. Our findings may be used to design a system with nontrivial electron correlations and functionalities.

Received 21 October 2017
Revised 11 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.241115

Physics Subject Headings (PhySH)

Ballistic transport Coulomb blockade Electrical conductivity

Quantum dots Two-dimensional electron gas

Spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Changki Hong¹, Gwangsu Yoo², Jinhong Park³, Min-Kyun Cho⁴, Yunchul Chung^1,3,*, H.-S. Sim^2,†, Dohun Kim^4,‡, Hyungkook Choi⁵, Vladimir Umansky³, and Diana Mahalu³

¹Department of Physics, Pusan National University, Busan 46241, Republic of Korea
²Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
³Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
⁴Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Republic of Korea
⁵Department of Physics, Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 54896, Republic of Korea

^*ycchung@pusan.ac.kr
^†hs_sim@kaist.ac.kr
^‡dohunkim@snu.ac.kr

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Issue

Vol. 97, Iss. 24 — 15 June 2018

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Images

Figure 1
(a) A scanning electron microscope (SEM) image of a similar device used in the experiment. The sample was fabricated on a GaAs/AlGaAs heterostructure wafer having a 78.5-nm-deep two-dimensional electron gas (2DEG) layer with carrier density $n = 2.2 \times 10^{11} {cm}^{- 2}$ and mobility $μ = 4.7 \times 10^{6} cm$ /V s. (b) The final device image with a metallic bridge floating over the QD structure to connect the island gate B. (c) To achieve the degeneracy for electron pairing, $E_{12}$ and $E_{13}$ are kept stronger than $E_{23}$ , where $E_{i j}$ is the electrostatic coupling energy between $QD i$ and $QD j$ . (d) Stability diagram as a function of $V_{P 2}$ and $V_{P 3}$ , where $V_{P i}$ is the voltage applied to the plunger gate of $QD i$ . $V_{P 1}$ is fixed at a value with which the degeneracy is obtained. It is computed for a TQD with the symmetry between QD2 and QD3, using Eq. (1). Electron occupation numbers are labeled as (0,0,0), for clarity, by subtracting constants from the actual numbers. The actual numbers are roughly larger than 100. The degeneracy for electron pairing occurs between (1,0,0) and (0,1,1) (see a red circle in the center), between $(1, - 1, 1)$ and (0,0,2) (the upper left-hand corner), and between $(1, 1, - 1)$ and (0,2,0) (the lower right-hand corner).
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Figure 2
In the upper panel, the occupation-number state $(n_{1}, n_{2}, n_{3})$ having the lowest electrostatic energy $U$ is presented along the line of $V \equiv a V_{P 1} = V_{P 2} = V_{P 3}$ . $a \approx 2.04$ is chosen such that the line passes through the center of a domain of $(V_{P 1}, V_{P 2}, V_{P 3})$ in which the states (1,0,0) and (0,1,1) are the degenerate ground states of $U$ . For each $(n_{1}, n_{2}, n_{3})$ , $U (n_{1}, n_{2}, n_{3})$ is plotted (parabolas) as a function of $V$ . Dashed lines indicate the values of $V$ at which a transition between different ground states occurs. The effective charges $Q_{1}$ (middle panel) and $Q_{2}$ (lower) are also plotted as a function of $V$ . This plot is drawn with the same parameters as Fig. 1.
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Figure 3
Stability diagram measured with varying $V_{P 2}$ and $V_{P 3}$ , at fixed $V_{P 1}$ at (a) $- 0.118$ , (c) $- 0.115$ , (d) $- 0.112$ , and (e) $- 0.109$ V. The black lines in (a) indicate the stability diagram calculated with the capacitances in Ref. [14]. The conductance measured only through QD2 and QD3 (G2+G3) is presented in the Supplemental Material [15]. (b) Dashed lines represent the charge degeneracy lines of QD1 (red), QD2 (blue), and QD3 (black). For all the figures, color scales are the same as the one in (a).
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Figure 4
Electron conductance through (a) QD1 only (G1), and that through (b) QD2 and QD3 (G2+G3), measured around the central region of Fig. 3. (c) Conductance through QD1, QD2, and QD3 can be measured as G1, G2, and G3, respectively. (d) Energy levels of the TQD around the EP degeneracy line, calculated with the same capacitances as those used for calculating the stability diagram in Fig. 3. The $x$ axis of the plot is scanned from the red point to the blue point in the inset. The orange point indicates the center of the EP degeneracy line of (0,1,1) and (1,0,0). (e) Conductance peaks (solid lines) of $G i$ 's measured along the line in the inset of (d). The peak center occurs at the EP degeneracy point. A conductance peak (dotted black lines) measured around a charge degeneracy line of each QD [e.g., around that of (0,0,0) and (1,0,0) for QD1] is shown for comparison. The voltage is converted into energy scale $α V_{P}$ by measuring $α$ [17] for each QD. The peaks are horizontally shifted such that their centers are located at the same position. Also, for clarity, the peaks of QD1 and QD2 are shifted vertically by $0.4 e^{2} / h$ and $0.2 e^{2} / h$ , respectively.
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Figure 5
(a) Couplings between the QDs are set opposite to the EP condition. (b) Measured conductance (G2+G3) through QD2 and QD3 in the case of (a). The white dashed line represents the charge degeneracy line of QD1 (separately measured). This line crosses the DQD degeneracy line of QD2 and QD3 at the center of the figure.
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