Observation of Aharonov-Bohm effect in PbTe nanowire networks

Letter

Observation of Aharonov-Bohm effect in PbTe nanowire networks

Zuhan Geng, Zitong Zhang, Fangting Chen, Shuai Yang, Yuying Jiang, Yichun Gao, Bingbing Tong, Wenyu Song, Wentao Miao, Ruidong Li, Yuhao Wang, Qinghua Zhang, Fanqi Meng, Lin Gu, Kejing Zhu, Yunyi Zang, Lin Li, Runan Shang, Xiao Feng, Qi-Kun Xue, Ke He, and Hao Zhang

Phys. Rev. B 105, L241112 – Published 22 June 2022

Abstract

We report phase coherent electron transport in PbTe nanowire networks with a loop geometry. Magnetoconductance shows Aharonov-Bohm (AB) oscillations with periods of $h / e$ and $h / 2 e$ in flux. The amplitudes of $h / 2 e$ oscillations are enhanced near zero magnetic field, possibly due to interference between time-reversal paths. Temperature dependence of the AB amplitudes suggests a phase coherence length $\sim 8 12 μ m$ at 50 mK. This length scale is larger than the typical geometry of PbTe-based hybrid semiconductor-superconductor nanowire devices.

Received 23 December 2021
Revised 13 February 2022
Accepted 13 June 2022

DOI:https://doi.org/10.1103/PhysRevB.105.L241112

Physics Subject Headings (PhySH)

Electrical conductivity Mesoscopics Quantum interference effects Quantum transport

Nanowires

Dilution refrigerator

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zuhan Geng^1,*, Zitong Zhang^1,*, Fangting Chen^1,*, Shuai Yang^1,2, Yuying Jiang¹, Yichun Gao¹, Bingbing Tong², Wenyu Song¹, Wentao Miao¹, Ruidong Li¹, Yuhao Wang¹, Qinghua Zhang³, Fanqi Meng³, Lin Gu³, Kejing Zhu², Yunyi Zang², Lin Li², Runan Shang², Xiao Feng^1,2,4, Qi-Kun Xue^1,2,4,5, Ke He^1,2,4,†, and Hao Zhang ^1,2,4,‡

¹State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
²Beijing Academy of Quantum Information Sciences, Beijing 100193, China
³Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁴Frontier Science Center for Quantum Information, Beijing 100084, China
⁵Southern University of Science and Technology, Shenzhen 518055, China

^*These authors contributed equally to this paper.
^†[email protected]
^‡[email protected]

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Vol. 105, Iss. 24 — 15 June 2022

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Images

Figure 1
(a) Pinch-off of a PbTe nanowire with the mobility fit (red line). Inset: Device SEM. (b) Cross-sectional HAADF with crystal directions labeled. (c) Enlarged HAADF of the orange box in (b). (d) SEM of device A (nanowire loop) and its 3D schematic.
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Figure 2
AB oscillations in device A. (a) Magnetoconductance, $B$ perpendicular to the substrate. Insets: Magnifications of the regions of $h / 2 e$ and $h / e$ oscillations. (b) Magnetoconductance, $B$ parallel to the substrate. $B$ is offset by 4 and 2 mT for (a) and (b), based on the symmetry of the WAL. (c) FFT of (a) (black) and (b) (red). (d) Two more AB curves, $B$ perpendicular to the substrate. (e) Black: Ensemble averaged FFT, after subtracting a conductance background (smooth window 1.42 mT). Blue: Ensemble averaged FFT by limiting the $B$ range below 5 mT. Red: Averaged FFT outside this range. (f) AB at a fixed in-plane $B$ of 30 mT. (g) FFT of (f). In (c), (e), and (g), boundaries of the shaded area are the geometric bounds estimated from the device SEM. $T \sim 20 mK$ .
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Figure 3
Temperature ( $T$ ) dependence of AB oscillations in device A. (a) $h / e$ oscillations at several $T s$ . $V_{TG} = 9.4 V$ . (b) AB after subtracting a background (smooth window 1.42 mT). (c) $h / 2 e$ oscillations (background subtracted) at three $T s$ . Vertical offsets are 0.025 and 0.045 ( $\times 2 e^{2} / h$ ) for clarity. $V_{TG} = 9.8 V$ . (d) $T$ dependence of the $h / e$ (left) and $h / 2 e$ (right) FFT amplitudes for all measured $T s$ . Red lines are fittings to extract the phase coherence length.
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Figure 4
AB effect in device B. (a) and (b) SEM before (a) and after (b) the fabrication of contacts (false colored yellow), dielectric, and top gate. (c) Magnetoconductance, $B$ perpendicular to the substrate. A narrower $B$ range is shown for clarity. Fridge temperature $\sim 40 mK$ . (d) and (e) Magnifications of (c) (see dashed boxes), corresponding to $h / e$ and $h / 2 e$ oscillations. (f) Magnification of a $B$ scan with a fixed in-plane $B$ of 10 mT. $V_{TG} = 16.6 V$ . $B$ offset is 5 mT for (c)–(f). (g) Black: FFT spectrum of (c). Red: FFT of a $B$ scan (not shown) at the same gate voltage but $B$ parallel to the substrate, serving as a control test. (h) FFT of (f) (the whole $B$ range). (i) $h / 2 e$ oscillations at three different $T s$ with background conductance subtracted. Background is smoothed over a window of 1.34 mT, close to the $h / e$ period estimated based on the inner surface loop area. Vertical offsets are 0.025 and 0.045 $\times 2 e^{2} / h$ for clarity. (j) $T$ dependence of the $h / 2 e$ FFT amplitudes. The fitting (red line) suggests a phase coherence length $\sim 9.2 μ m$ at 50 mK.
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