Imaging of Submicroampere Currents in Bilayer Graphene Using a Scanning Diamond Magnetometer

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Imaging of Submicroampere Currents in Bilayer Graphene Using a Scanning Diamond Magnetometer

M.L. Palm, W.S. Huxter, P. Welter, S. Ernst, P.J. Scheidegger, S. Diesch, K. Chang, P. Rickhaus, T. Taniguchi, K. Watanabe, K. Ensslin, and C.L. Degen

Phys. Rev. Applied 17, 054008 – Published 5 May 2022

Abstract

We report on nanometer magnetic imaging of two-dimensional current flow in bilayer graphene devices at room temperature. By combining dynamical modulation of the source-drain current with ac quantum sensing of a nitrogen-vacancy center in the diamond probe tip, we acquire magnetic field and current density maps with excellent sensitivities of 4.6 nT and $20 nA / μ m$ , respectively. The spatial resolution is 50–100 nm. We introduce a set of methods for increasing the technique’s dynamic range and for mitigating undesired back-action of magnetometry operation (scanning tip, laser and microwave pulses) on the electronic transport. Finally, we show that our imaging technique is able to resolve small variations in the current flow pattern in response to changes in the background potential. Our experiments demonstrate the feasibility for detecting and imaging subtle spatial features of nanoscale transport in two-dimensional materials and conductors.

Received 25 January 2022
Accepted 28 March 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.054008

Physics Subject Headings (PhySH)

Classical transport Electrical conductivity Magnetic texture Photocurrent Quantum sensing

Bilayer graphene Nitrogen vacancy centers in diamond

Scanning techniques

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

M.L. Palm ^1,§, W.S. Huxter ^1,§, P. Welter ¹, S. Ernst¹, P.J. Scheidegger ¹, S. Diesch¹, K. Chang^1,†, P. Rickhaus^1,‡, T. Taniguchi², K. Watanabe ³, K. Ensslin ^1,4, and C.L. Degen ^1,4,*

¹Department of Physics, ETH Zurich, Otto Stern Weg 1, Zurich 8093, Switzerland
²International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
³Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁴Quantum Center, ETH Zurich, Zurich 8093, Switzerland

^*degenc@ethz.ch
^†Present address: Aeva Inc., 555 Ellis St., Mountain View, CA 94043, USA.
^‡Present address: Qnami AG, Hofackerstrasse 40B, 4132 Muttenz, Switzerland.
^§These authors contributed equally.

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Vol. 17, Iss. 5 — May 2022

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Images

Figure 1
Schematic of the current imaging experiment. (a) We use a nitrogen-vacancy center (red) in a diamond tip (gray) to image the magnetic stray field appearing above a current-carrying graphene device. Microwave (dark red) and laser pulses (green) are used to manipulate and read out the spin state of the N- $V$ center [22]. The device consists of a bilayer graphene (BLG) sheet encapsulated in hexagonal boron nitride ( $h$ -BN, 11 nm top and 27 nm bottom thickness) that sits on top of a graphite back gate (BG). $V_{S D}$ and $V_{BG}$ are source-drain and back-gate voltages, respectively. (b,c) Atomic force microscopy images of the two devices used in this study. Note that device A is only partially covered by the back gate (white dashed line). Electrical contacts are numbered. Scale bars are $2 μ m$ . (d) Measurement protocol. We modulate the source-drain voltage $V_{S D}$ (orange), microwave power (red), laser power (green) and back-gate voltage $V_{BG}$ (purple) using an arbitrary waveform generator. Tall microwave pulses are $π$ rotations and short pulses are $π / 2$ rotations. Labels $x, y, - x, - y$ indicate the pulse phase $Φ$ . $τ$ is the phase accumulation time of the dynamical decoupling sequence (here a spin echo). $C_{ref}^{0}$ and $C_{ref}^{1}$ are reference photoluminescence intensities of the two spin states. Triggers indicate the start of a measurement cycle. (e) Measured source-drain current during the experimental protocol (d). The inset shows the effect of laser pulses (on, off) when the tip is positioned near one of the injection points at $V_{S D} = 0 V$ (10-point moving-average filter applied). $2 I_{S D}$ is the peak-to-peak amplitude of the current signal.
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Figure 2
Correlative maps of magnetometry and transport characteristics. (a) Quantum phase recorded by the scanning magnetometer, according to Eqs. (2)–(3). (b) Topography recorded by the position feedback of the scanning magnetometer. (c) Alternating current amplitude of the source-drain current. (d),(e) Direct current offset of the source-drain current while the laser is (d) off and (e) on (see [28] for more details). Global offsets have been subtracted from both images. (f) Rabi frequency of the N- $V$ spin, recorded separately. Scale bars are $1 μ m$ .
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Figure 3
Phase-unwrapping and current-density reconstruction. (a)–(c) Variable grid size method, demonstrated on device B with $I_{S D} \approx 7.2 μ A$ between contacts 1 and 2. (a) Map of the quantum phase composed of three scans (I–III) with varying pixel sizes (I, $100 \times 100 nm$ ; II, $19 \times 33 nm$ ; III, $20 \times 10 nm$ ). Gray markers denote the subsection of the image processed in (b),(c). (b) Map of the magnetic field after applying a phase unwrapping algorithm. $B$ represents the vector field component along the N- $V$ center’s anisotropy axis [28]. (c) Map of the current density reconstructed from (b). (d)–(g) Bayesian inference method, demonstrated on device A with $I_{S D} \approx 10 μ A$ between contacts 1 and 3. (d) Maps of the quantum phase recorded with $τ_{1} = 10 μ s$ and $τ_{2} = 20.5 μ s$ . (e) Map of the magnetic field after the first phase-unwrapping step. (f) Map of the magnetic field after the second phase-unwrapping step that corrects for spatial smoothness. (g) Map of the current density. Dashed white boxes in (c),(g) refer to Fig. 4. Filter cutoff in (c),(g) is $λ = z$ , where $z$ is the standoff distance. Scale bars are $1 μ m$ .
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Figure 4
Transport physics. (a) Magnified current density map of device A [dotted area in Fig. 3]. Arrows indicate anomalies in the current flow. (b) Corresponding AFM topography. (c) Current density map of device B [dash-dotted area in Fig. 3]. Upper map shows the experimental data. Lower map shows simulated data assuming a perfect rectangular conductor after adding the equivalent amount of white noise. Arrows indicate channels of increased current flow in the experiment. (d) Current density map of device A [dashed area in Fig. 3] for $V_{BG} = 0 V$ . Note that the back gate only covers the right part of the device, indicated by a dashed line. (e) Differential current density map $Δ J_{y}$ obtained by subtracting $J_{y}^{(V_{BG} = - 2 V)} - J_{y}^{(V_{BG} = 0 V)}$ . (f) Reconstructed current density profiles $J_{y}$ across the Hall-bar channel (device B). Dots are the data and solid line is a calculation for a uniform current density profile. $I_{S D}$ is the applied source-drain current. Step size is $10 nm$ for the $I_{S D} = 23.5 μ A$ curve and $40 nm$ for all other curves. Curves are vertically offset for clarity. Scale bars are $500 nm$ .
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Figure 5
Imaging of a $0.3 μ A$ current. (a),(b) High-sensitivity magnetic field and current density maps recorded on device A. A current of $I_{S D} = 0.3 μ A$ and $f = 1.33 MHz$ is injected into terminal 1 and collected at terminal 3. Some current leakage through the floating terminals 2 and 4 is also observed. Data are recorded using a dynamical decoupling sequence with $N = 128$ refocusing pulses and $τ = 48 μ s$ . Scale bars are $1 μ m$ and filter cutoff in (b) is $λ = 1.5 z$ . (c) Best-effort magnetic line scan along the dashed line in (a). For this scan, current is injected into terminal 2 and collected at terminal 1, and measurement parameters are $N = 128$ , $τ = 38 μ s$ , and $f = 1.68 MHz$ . Each pixel represents a 120 s average. The upper trace (vertically offset for clarity) shows the difference between two line scans. The standard deviation extracted from the point-to-point difference is $σ_{B} = 4.6 nT$ [28]. (d) Corresponding current density line scan with a standard deviation of $σ_{J_{x}} = 20 nA / μ m$ .
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