Pulsed-gate spectroscopy of single-electron spin states in bilayer graphene quantum dots

Letter

Pulsed-gate spectroscopy of single-electron spin states in bilayer graphene quantum dots

L. Banszerus, K. Hecker, E. Icking, S. Trellenkamp, F. Lentz, D. Neumaier, K. Watanabe, T. Taniguchi, C. Volk, and C. Stampfer

Phys. Rev. B 103, L081404 – Published 16 February 2021

Abstract

Graphene and bilayer graphene quantum dots are promising hosts for spin qubits with long coherence times. Although recent technological improvements make it possible to confine single electrons electrostatically in bilayer graphene quantum dots and their spin and valley texture of the single-particle spectrum has been studied in detail, their relaxation dynamics remains still unexplored. Here, we report on transport through a high-frequency gate-controlled single-electron bilayer graphene quantum dot. By transient current spectroscopy of single-electron spin states, we extract a lower bound of the spin relaxation time of 0.5 $μ s$ . This result represents an important step towards the investigation of spin coherence times in graphene-based quantum dots and the implementation of spin qubits.

Received 4 December 2020
Revised 27 January 2021
Accepted 3 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L081404

Physics Subject Headings (PhySH)

Coulomb blockade Spin dynamics

Graphene Quantum dots

Spin

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Banszerus ^1,2,*, K. Hecker ¹, E. Icking^1,2, S. Trellenkamp³, F. Lentz³, D. Neumaier⁴, K. Watanabe ⁵, T. Taniguchi⁶, C. Volk ^1,2, and C. Stampfer ^1,2

¹JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU
²Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
³Helmholtz Nano Facility, Forschungszentrum Jülich, 52425 Jülich, Germany, EU
⁴AMO GmbH, Gesellschaft für Angewandte Mikro- und Optoelektronik, 52074 Aachen, Germany, EU
⁵Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁶International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*luca.banszerus@rwth-aachen.de

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Issue

Vol. 103, Iss. 8 — 15 February 2021

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Images

Figure 1
(a) Schematic of the device. A combination of a graphite back gate and split gates (SGs) are used to form a narrow conductive channel in the bilayer graphene. The finger gate (FG) is used to define the quantum dot and is connected to a bias tee, allowing application of AC pulses and DC voltages to the same gate. Inset: Illustration of a square pulse with pulse widths $τ_{A}$ and $τ_{B}$ and amplitude $V_{A}$ . (b) False-color atomic force micrograph of the device showing the split gates and six finger gates (the FG used for the experiment is highlighted). (c) Band edge diagram along the channel, illustrating the formation of a QD induced by a positive $V_{FG}$ pushing the conduction band edge below the Fermi level $E_{F}$ . (d) Conductance $G$ as a function of $V_{FG}$ at a bias voltage of $V_{b} = 0.3$ mV. Numbers indicate the electron occupation $N$ of the QD in the regions of the Coulomb blockade. Inset: Finite-bias spectroscopy $d I / d V_{b}$ data. The scale bar corresponds to $Δ V_{FG} = 100$ mV.
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Figure 2
(a) Conductance of the sixth Coulomb peak as a function of $V_{FG}$ while applying a square pulse with a frequency of $100 kHz$ and $50 %$ duty cycle. Different traces correspond to AC amplitudes of $V_{A} =$ 0 V (blue), 1 V (purple), and 2 V (black). Peak B at lower $V_{FG}$ originates from tunneling events taking place during $τ_{B}$ , and peak A at higher $V_{FG}$ originates from tunneling events during $τ_{A}$ (see inset). (b) Conductance as a function of $V_{FG}$ and $V_{A}$ for the first four Coulomb peaks. The arrows correspond to the $V_{A}$ values shown in (a).
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Figure 3
(a) Average number of electrons $〈 n 〉$ tunneling through the QD per pulse cycle as a function of $Δ V_{FG}$ and $V_{A}$ for the first Coulomb peak (transition from $N = 0$ to 1 electrons). $V_{b} = 100 μ V, B_{⊥} = 1.5$ T, and $f = 6.26$ MHz. Only GS transport is visible during $τ_{A}$ and $τ_{B}$ (white dashed lines). (b) Measurement as in (a), performed at $B_{⊥} = 1.8$ T. Transient currents via ESs become visible. (c) Finite-bias spectroscopy showing the differential conductance in the absence of a pulsed-gate voltage ( $V_{A} = 0$ ) at the transition from $N = 0$ to 1. The blue, purple, and red dashed lines highlight the first three ESs ( $B_{⊥} = 1.8$ T). The inset shows the current along a cut at $Δ V_{FG} = 5$ mV, highlighting the asymmetry of the tunneling barriers [29]. (d) Energy difference between the different ESs and the GS measured as a function of the total magnetic field $| B |$ . The in-plane magnetic field $B_{∥}$ is varied at a constant $B_{⊥} = 1.8$ T. The black dashed lines correspond to the Zeeman energy shift with a $g$ factor of 2. (e) $〈 n 〉$ per pulse cycle as a function of $Δ V_{FG}$ and $τ_{B}$ at $τ_{A} = 1 μ s, V_{A} = 1.2$ V, $B_{⊥} = 1.8$ T, and $B_{∥} = 350$ mT. (f) $〈 n 〉$ per pulse cycle averaged over all $τ_{B}$ as a function of $Δ V_{FG}$ . The dashed lines correspond to GS and ES marked in (b) and (c).
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Figure 4
(a) Average number of electrons $〈 n 〉$ passing through the QD via the GS as a function of $τ_{B}$ . From the linear slope, we extract the combined tunneling rate $Γ$ . Top left: Schematic representation of the initialization (emptying) of the QD during $τ_{A}$ . Top right: Possible tunneling processes during $τ_{B}$ leading to a steady current through the GS. (b)–(d) Average number of electrons passing through the QD via ${ES}_{1}, {ES}_{2}$ , and ${ES}_{3}$ as a function of $τ_{B}$ . $〈 n 〉$ /pulse saturates after the characteristic blocking time $1 / γ_{i}$ . Solid lines show fits to the experimental data according to $〈 n 〉$ /pulse $= Γ (1 - e^{- τ_{B} γ_{i}})$ . Top left: Schematic representations of the possible tunneling and relaxation processes during $τ_{B}$ for transport through the ES(s). Top right: Blocking of the tunneling current due to the occupation of the GS and/or ES(s) below the bias window.
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