Transport through a network of two-dimensional NbC superconducting crystals connected via weak links

Meng Hao, Chuan Xu, Zhen Liu, Cheng Wang, Zhibo Liu, Su Sun, Hui-Ming Cheng, Wencai Ren, and Ning Kang

Phys. Rev. B 101, 115422 – Published 23 March 2020

Abstract

Recent progresses in the growth and fabrication techniques for preparing crystalline two-dimensional (2D) superconductors have stimulated intense interest in the studies of the electronic properties of these systems. Here we investigate the superconducting transport properties based on chemical vapor deposition-grown thin NbC crystals consisting of network structures. The 2D character of the superconductivity in individual NbC crystals is revealed by examining the angular dependence of magnetotransport measurements. At low temperatures, the samples show nonmonotonic double-step superconducting transitions as a function of temperature and magnetic field. We demonstrate that the observed transport characteristics can be understood in terms of coupled Josephson junctions forming between isolated NbC crystals, including the effects of Josephson and quasiparticle tunneling. In particular, detailed analysis of the magnetic field-driven transition suggests the existence of quantum flux-creep regime at low temperatures and small magnetic fields in such thin NbC superconducting crystals. Our work underlines the importance of the morphology on the transport properties of 2D superconducting crystals, providing a comprehensive understanding of crystalline 2D superconductors.

Received 22 September 2019
Revised 18 January 2020
Accepted 2 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115422

Physics Subject Headings (PhySH)

Superconducting fluctuations Superconducting phase transition

2-dimensional systems Josephson junctions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Meng Hao¹, Chuan Xu², Zhen Liu¹, Cheng Wang¹, Zhibo Liu², Su Sun ², Hui-Ming Cheng², Wencai Ren^2,*, and Ning Kang ^1,†

¹Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China
²Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

^*Corresponding author: wcren@imr.ac.cn
^†Corresponding author: nkang@pku.edu.cn

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Vol. 101, Iss. 11 — 15 March 2020

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Images

Figure 1
(a) Optical image of reticular 2D NbC crystals on growth substrate. (b) Low magnification and (c) high magnification SEM images of the reticular NbC crystals on growth substrate. (d) Low magnification HAADF-STEM image of a hexagonal 2D NbC crystal transferred onto TEM grid. (e) Corresponding SAED pattern and (f) high-resolution HAADF-STEM image of an individual 2D NbC crystal along [111] zone axis.
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Figure 2
(a) Temperature dependence of four-terminal resistance for a typical NbC sample with a thickness of 12 nm, measured in the temperature range of 1.8–300 K at zero magnetic field. Inset shows expanded view of $R (T)$ curve between 1.8 and 10 K, exhibiting two-step superconducting transitions. The arrows indicate two characteristic transition temperatures $T_{c 1}$ and $T_{c 2}$ , respectively. (b) Superconducting resistive transition under different applied magnetic fields of 0, 0.5, and 3.0 T, respectively. The nonmonotonic resistive transition at zero magnetic field can be divided into three temperature regions, highlighted in blue, yellow, and red backgrounds, respectively.
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Figure 3
(a) Magnetic field dependence of the resistance for different tilting angles $θ$ , obtained at 1.9 K. The inset illustrates the measurement configuration. The $θ$ is the angle between the applied field and the sample plane. As the magnetic field is titled toward the sample plane $(θ \to 0)$ , the resistive transitions gradually shift to the higher magnetic fields. (b) Angle dependence of upper critical field $H_{c}$ deduced from higher resistive transition region. The blue dashed line is the fitting result using the Tinkham model with Eq. (1) for 2D superconductors.
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Figure 4
(a) Resistance of two-dimensional NbC network as a function of temperature under several magnetic fields, applied perpendicular to the sample plane. (b) Schematics of the formation of Josephson junctions in the network of 2D NbC islands. The triangle shapes represent 2D superconducting NbC crystals. In an intermediate temperature regime (region II), quasiparticle tunneling between NbC islands dominates the charge transport exhibiting a quasireentrant behavior $(d R / d T < 0$ ). With further decreasing temperature, Josephson couplings between NbC islands become significant and global superconductivity begins to occur. (c) The semi-logarithmic plot of the resistance as as function of temperature. One can see the $R (T)$ curves at lower temperatures (region III) for various magnetic fields are in good agreement with an inverse Arrhenius relation, $R = R_{0} exp (T / T_{0})$ . Inset: Plot of the extracted $T_{0}$ as a function of magnetic field. The dashed line is provided as a guide for the eye, indicating a monotonically decreasing $T_{0}$ with $H$ .
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Figure 5
(a) Magnetoresistance curves of two-dimensional NbC network at various temperatures from 1.9 to 7.0 K. The curves are successively shifted vertically for clarity. The arrows indicate the appearance of the resistance peak below 3 K, exhibiting a nonmonotonic dependence on magnetic field. With increasing temperature, the resistance peak is shifted towards zero magnetic field. (b) Low-field magnetoresistance at 1.9 K. The red solid line is a fit to the data using the quantum flux-creep model according to Eq. (3). Inset: Low-field resistance as a function of perpendicular component of magnetic field at various tilting angles $θ$ for sample 1. (c) High magnetic field portion of the measured $R (H)$ curves from 1 to 2 T at various temperatures, plotted on a log-log scale. The dashed lines are guides to the eye, indicating a power-law dependence $H^{α}$ . Inset: The obtained power-law exponent $α$ as a function of temperature.
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