Counting statistics of single electron transport in bilayer graphene quantum dots

Open Access

Counting statistics of single electron transport in bilayer graphene quantum dots

Rebekka Garreis, Jonas Daniel Gerber, Veronika Stará, Chuyao Tong, Carolin Gold, Marc Röösli, Kenji Watanabe, Takashi Taniguchi, Klaus Ensslin, Thomas Ihn, and Annika Kurzmann

Phys. Rev. Research 5, 013042 – Published 24 January 2023

Abstract

We measure telegraph noise of current fluctuations in an electrostatically defined quantum dot in bilayer graphene by real-time detection of single electron tunneling with a capacitively coupled neighboring quantum dot. Suppression of the second and third cumulant (related to shot noise) in a tunable graphene quantum dot is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels. Furthermore, we use this method to investigate the first spin excited state, an essential prerequisite to measure spin relaxation.

Received 14 October 2022
Revised 23 December 2022
Accepted 4 January 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.013042

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Coulomb blockade Quantum transport Shot noise

Bilayer graphene Nanostructures Quantum dots

Transport techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rebekka Garreis ^1,*, Jonas Daniel Gerber ¹, Veronika Stará ², Chuyao Tong ¹, Carolin Gold ^1,3, Marc Röösli¹, Kenji Watanabe ⁴, Takashi Taniguchi ⁴, Klaus Ensslin ¹, Thomas Ihn¹, and Annika Kurzmann^1,5

¹Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
²Central European Institute of Technology, Brno University of Technology, 612 00 Brno, Czech Republic
³Department of Physics and Astronomy, Columbia University, New York NY 10027, USA
⁴National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁵2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany

^*garreisr@phys.ethz.ch

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Vol. 5, Iss. 1 — January - March 2023

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Images

Figure 1
(a) False-color micrograph of the device. The quantum dot (QD) is defined between two tunnel barriers (TL and TR), and its chemical potential is tuned by the plunger gate voltage $V_{PG}$ . A second capacitively coupled dot formed underneath the finger gate (FG) is used as a charge detector. (b) Time traces of the voltage drop in the detector corresponding to charge fluctuations between an empty dot and one electron in the dot for three different $V_{PG} s$ and corresponding level schematics. Top: The chemical potential of the quantum dot is above the chemical potential of source and drain. Middle: The chemical potentials of the dot, source, and drain are aligned. Bottom: The chemical potential of the quantum dot is below the chemical potential of source and drain. (c) Probability density of the times $τ_{in}$ and $τ_{out}$ obtained from the time trace shown in the top panel of (b) with a time bin size of $0.013 s$ . (d) Evolution of the tunneling rates versus plunger gate detuning from the center of the resonance $Δ V_{PG}$ . Fitting a Fermi-Dirac distribution yields an electron temperature of $52 (3) mK$ .
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Figure 2
(a) Evolution of the tunneling rates versus energy detuning $Δ E$ with a finite bias applied to the dot. The center plateau corresponds to the finite bias window. Inset: Time trace corresponding to an energy detuning around zero. The time trace is divided into subtraces of length $t_{0}$ and the number of events $n$ , i.e., steps up (marked with arrows) per time period is counted. (b) Statistical distribution of the number $n$ of electrons leaving the quantum dot during a given time period $t_{0}$ . We extract the first three cumulants of this distribution. (c) Second and third normalized cumulants of the distribution of $n$ as a function of the asymmetry of the tunneling rates. To improve the statistics, each point at a certain asymmetry is the mean of all time traces obtained within the bias window for given tunnel barrier voltages.
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Figure 3
(a) Time trace for a two-level pulse applied to the plunger gate. The signal is color coded by the parts where the electrochemical potential of the quantum dot is above (olive) and below (green) the electrochemical potential of source and drain. The pulse sequence is plotted in blue. (b) Same time trace as shown in (a), but separated into the two regimes of total $Δ E$ to be analyzed individually. (c) Tunneling rates versus energy detuning for an unpulsed measurement. (d) Tunneling rates for the same gate configuration as in (c), but with an additional square pulse applied to the plunger gate. The resolution for energies where the Fermi-Dirac distribution is at the higher plateau is increased considerably. The green and olive lines mark the pulsed energy configuration of the trace shown in (a) and (b).
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Figure 4
(a) Measured $d V_{\det} / d V_{PG}$ at finite bias for the first charge carrier transition. The spin excited state is marked with an arrow. (b) Schematic energy diagram of the quantum dot including the first spin excited state. Possible tunneling and relaxation paths are labeled. (c)–(f) Tunneling rates versus energy detuning for different source drain biases as indicated in (a). As soon as the spin excited state enters the bias window, the additional tunneling path yields an increased tunneling-in rate.
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