Visualizing the merger of tunably coupled graphene quantum dots

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Visualizing the merger of tunably coupled graphene quantum dots

Daniel Walkup, Fereshte Ghahari, Steven R. Blankenship, Kenji Watanabe, Takashi Taniguchi, Nikolai B. Zhitenev, and Joseph A. Stroscio

Phys. Rev. B 108, 235407 – Published 6 December 2023

Abstract

We examine graphene quantum dots in back-gated devices on hexagonal boron nitride (hBN) and visualize their merger using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy. These dots are formed by the combination of nanoscale potential wells created by pulsing the voltage of an STM tip above charged defects in the hBN underlayer, and strong magnetic fields gapping the density of states, which add insulating rings in the potential wells. Control of the charge state is achieved via the back gate and sample bias voltages, and the position of the STM tip which serves as a mobile top gate. The individual quantum dots present a distinct phenomenology of single-electron charging due to multiple Landau levels crossing the Fermi energy concentrically. Here, we study side by side pairs of these quantum dots via STM, where we observe a tunable interdot coupling and mergeability. Specifically, with increasing charge filling, the quantum dots formed by electrons belonging to one Landau level merge into a single quantum dot, while the electrons in the next-higher Landau level remain spatially separated into two charge pockets. Using the probe tip as a multifunction tool, we visualize the evolution, growth, and merger of this unique double quantum dot system as a function of tip position and gate voltages.

Received 23 June 2023
Revised 6 October 2023
Accepted 13 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.235407

Physics Subject Headings (PhySH)

Graphene Quantum dots

Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel Walkup ^1,*,†, Fereshte Ghahari^1,2,*, Steven R. Blankenship¹, Kenji Watanabe ³, Takashi Taniguchi⁴, Nikolai B. Zhitenev ¹, and Joseph A. Stroscio ¹

¹Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
²Department of Physics, George Mason University, Fairfax, Virginia 22030, USA
³Research Center for Electronic and Optical Materials, National Institute for Materials Science; 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
⁴Research Center for Materials Nanoarchitectonics, National Institute for Materials Science; 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

^*These authors contributed equally to this work.
^†daniel.walkup@nist.gov

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Issue

Vol. 108, Iss. 23 — 15 December 2023

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Images

Figure 1
Back-gated graphene device used to create the double quantum dot. (a) Cross-sectional view of the graphene device including STM tip. (b) Optical microscope image of the device; bright green is hBN, yellow is the Au landing pad.
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Figure 2
Schematic of the graphene Landau level double quantum dot (DQD). (a), (c) Top-view schematics showing the compressible areas where labeled Landau levels cross the Fermi energy, with gate voltage decreasing from (a) to (c) in a $p$ -type potential well. (b), (d) Energy-displacement schematic through the center of the two dots. The $Y$ axis of (b), (d) is aligned with that of (a), (c), and the latter represent the Fermi-energy slices of the energy diagrams (b), (d) respectively. The islands formed by the $N = 0$ Landau level merge between (a) and (c), and (b) and (d).
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Figure 3
Spatial tunneling measurements of a graphene double quantum dot (DQD). (a) STM topography showing the area of the graphene DQD at zero magnetic field. Tunneling set point: Current $I = 50$ pA, $V_{b} = - 100 mV, V_{g} = 12$ V. (b)–(h) Spatial map of the $dI / dV$ signal in the DQD at fixed sample bias $V_{b} = - 150 mV$ and gate voltage $V_{g}$ indicated in each panel. As the tip gates the dots, concentric rings correspond to single-electron charging events. The dashed yellow circles in (b) outline the areas of dot 1 and dot 2. Tunneling set point: Current $I$ = 80 pA, $V_{b} = - 150 mV$ . (i) Series of $dI / dV$ versus $V_{g}$ curves as a function of the $Y$ -axis tip position along the green dashed line at $X$ = 70 nm in (b) and the same fixed sample bias. The regions of separate dots, coupled dots, and a merged dot are indicated by yellow, blue, and red ovals, respectively. Temperature $T$ = 4.3 K in all panels, magnetic field, $B$ = 8 T in panels (b)–(i).
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Figure 4
Single-electron charging measurements of the double quantum dot. (a) Series of $dI / dV$ versus $V_{g}$ curves as a function of the $Y$ -axis tip position obtained in the center of the dot at $X$ = 70 nm in Fig. 3 and fixed sample bias $V_{b} = - 150 mV$ . (b)–(f) $dI / dV$ measurements in the $V_{b}, V_{g}$ plane at the tip positions indicated by green×'s in (a). Moving from (b) to (f) up the $Y$ axis, the tip departs dot 2 and moves toward dot 1, with corresponding changes in the slopes of the two series of charging lines belonging to dot 1 and dot 2 [yellow and cyan dashed lines, respectively, in (d), (f)]. Avoided crossings are visible, illustrated by the arrows in (d), (f). Regions of weakly coupled dots and nearly merged dots are circled in blue and green in (d), respectively. Tunneling set point: Current $I$ = 150 pA, $V_{b} =$ 300 mV. Temperature $T$ = 4.3 K, magnetic field, $B$ = 8 T.
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Figure 5
Model calculations for charge stability diagrams of the double quantum dot DQD. (a) An expanded section of data in Fig. 3, with labels indicating the hexagonal cells whose dimensions were used to estimate capacitances and to generate the simulated charge-stability diagram of a fixed-size DQD in (b)–(d). The diagrams show the lines becoming more parallel in going from (b) to (d), indicating the increased interdot coupling (f). The panels (b)–(d) use capacitances estimated from cells labeled 1, 6, and 14 in (a), respectively. The estimated model parameters are shown in (e), (f) and the slopes of the charging lines are shown in (g).
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